Rehovot 76100, Israel ; Helton, J. William(1-UCSD)
Department of Mathematics, University of California, San Diego
La Jolla, California, 92093 ; McCullough, Scott(1-FL)
Department of Mathematics, University of Florida
Gainesville, Florida, 32611
Non-commutative polynomials with convex level slices. (English summary)
Indiana Univ. Math. J. 66 (2017), no. 6, 2071-2135.
47L10 (90C22)
3646877
Helton, J. William(1-UCSD) Department of Mathematics, University of California, San Diego
La Jolla, California, 92093 ; Klep, Igor(NZ-AUCK)
Department of Mathematics, University of Auckland
Auckland, New Zealand ; McCullough, Scott(1-FL)
Department of Mathematics, University of Florida
Gainesville, Florida, 32611 ;
The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. (English summary)
J. Eur. Math. Soc. (JEMS) 19 (2017), no. 6, 1845-1897.
46B25 (14P10 52A20 90C22)
3646877
Helton, J. William(1-UCSD) Department of Mathematics, University of California, San Diego
La Jolla, California, 92093 ; Klep, Igor(NZ-AUCK)
Department of Mathematics, University of Auckland
Auckland, New Zealand ; McCullough, Scott(1-FL)
Department of Mathematics, University of Florida
Gainesville, Florida, 32611 ;
The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. (English summary)
J. Eur. Math. Soc. (JEMS) 19 (2017), no. 6, 1845-1897.
46B25 (14P10 52A20 90C22)
3543810
Evert, Eric(1-UCSD); Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL)
Circular free spectrahedra. (English summary)
J. Math. Anal. Appl. 445 (2017), no. 1, 1047-1070.
14A22 (14P10)
3543810
Evert, Eric(1-UCSD); Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL)
Circular free spectrahedra. (English summary)
J. Math. Anal. Appl. 445 (2017), no. 1, 1047-1070.
14A22 (14P10)
3530668
Augat, M.(1-FL); Balasubramanian, S.(6-IITM); McCullough, Scott(1-FL)
Compact sets in the free topology. (English summary)
Linear Algebra Appl. 506 (2016), 6-9.
47A20 (46L07 47A13)
3466819
Klep, Igor(NZ-AUCK); McCullough, Scott A.(1-FL); Nelson, Christopher S.(1-UCSD)
On trace-convex noncommutative polynomials. (English summary)
Michigan Math. J. 65 (2016), no. 1, 131-146.
16S10 (14P10 16Z05)
3451871
Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL)
Matrix convex hulls of free semialgebraic sets. (English summary)
Trans. Amer. Math. Soc. 368 (2016), no. 5, 3105-3139.
46L07 (13J30 14P10 46L89 90C22)
3439202
McCullough, Scott(1-FL); Russo, Benjamin(1-FL)
The 3-isometric lifting theorem. (English summary)
Integral Equations Operator Theory 84 (2016), no. 1, 69-87.
47A45 (34B24 47A20 47B99)
3318427
Cimprič, J.(SV-LJUB); Helton, J. W.(1-UCSD); McCullough, S.(1-FL); Nelson, C.(1-UCSD)
Real nullstellensatz and $*$-ideals in $*$-algebras. (English summary)
Electron. J. Linear Algebra 30 (2015), 19-50.
16S10 (16W10 16Z05)
3236407
Helton, J. William(1-UCSD); McCullough, Scott(1-FL)
Free convex sets defined by rational expressions have LMI representations. (English summary)
J. Convex Anal. 21 (2014), no. 2, 425-448.
47A63 (47L07)
3209314
Balasubramanian, S.(6-ISER-MS); McCullough, S.(1-FL)
Quasi-convex free polynomials. (English summary)
Proc. Amer. Math. Soc. 142 (2014), no. 8, 2581-2591.
16S36 (08B20 15A24 47A63)
3120628
Cimprič, Jakob(SV-LJUB); Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL); Nelson, Christopher(1-UCSD)
On real one-sided ideals in a free algebra. (English summary)
J. Pure Appl. Algebra 218 (2014), no. 2, 269–284.
14P10 (13J30)
3050247
Helton, William(1-UCSD-NDM); Klep, Igor(NZ-AUCK-NDM); McCullough, Scott(1-FL-NDM)
Free convex algebraic geometry. (English summary) Semidefinite optimization and convex algebraic geometry, 341–405,
MOS-SIAM Ser. Optim., 13, SIAM, Philadelphia, PA, 2013.
14A22 (14P05 14P10)
3066748
Cimprič, Jakob(SV-LJUB); Helton, J. William(1-UCSD); McCullough, Scott(1-FL); Nelson, Christopher(1-UCSD)
A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: algorithms. (English summary)
Proc. Lond. Math. Soc. (3) 106 (2013), no. 5, 1060–1086.
16W10 (16S10 47L30)
3034812
Helton, J. William(1-UCSD); Klep, Igor(SV-LJUBMP-NDM); McCullough, Scott(1-FL)
The matricial relaxation of a linear matrix inequality. (English summary)
Math. Program. 138 (2013), no. 1-2, Ser. A, 401–445.
90C22 (14P10 15A39)
2950768
Helton, J. William(1-UCSD-NDM); McCullough, Scott(1-FL-NDM)
Every convex free basic semi-algebraic set has an LMI representation. (English summary)
Ann. of Math. (2) 176 (2012), no. 2, 979–1013.
14Pxx
2962784
Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL)
Free analysis, convexity and LMI domains. (English summary) Mathematical methods in systems, optimization, and control, 195–219,
Oper. Theory Adv. Appl., 222, Birkhäuser/Springer Basel AG, Basel, 2012.
46L52 (32A10 47A56)
2935397
Helton, J. William(1-UCSD); Klep, Igor(NZ-AUCK); McCullough, Scott(1-FL)
The convex Positivstellensatz in a free algebra. (English summary)
Adv. Math. 231 (2012), no. 1, 516–534.
14P10 (13J30 46L07)
2904607
McCullough, Scott(1-FL); Sultanic, Saida
Agler-commutant lifting on an annulus. (English summary)
Integral Equations Operator Theory 72 (2012), no. 4, 449–482.
47A20
2899979
Jury, Michael T.(1-FL); Knese, Greg(1-AL); McCullough, Scott(1-FL)
Nevanlinna-Pick interpolation on distinguished varieties in the bidisk. (English summary)
J. Funct. Anal. 262 (2012), no. 9, 3812–3838.
47J99 (30E05 32A36 32E30)
2894701
Helton, J. William(1-UCSD); Klep, Igor(SV-LJUBMP-NDM); McCullough, Scott(1-FL)
Convexity and semidefinite programming in dimension-free matrix unknowns. Handbook on semidefinite, conic and polynomial optimization, 377–405,
Internat. Ser. Oper. Res. Management Sci., 166, Springer, New York, 2012.
90C22 (90C25)
2876487
McCullough, S.(1-FL); Trent, T. T.(1-AL)
The Douglas property for multiplier algebras of operators. (English summary)
J. Math. Anal. Appl. 389 (2012), no. 1, 130–137.
47A62 (30H50 32A37)
3020690
Dym, Harry(IL-WEIZ); Helton, J. William(1-UCSD); McCullough, Scott(1-FL)
Non-commutative varieties with curvature having bounded signature. (English summary)
Illinois J. Math. 55 (2011), no. 2, 427–464 (2012).
47A63 (47L30)
2749435
Helton, J. William(1-UCSD); Klep, Igor(SV-LJUBM); McCullough, Scott(1-FL)
Proper analytic free maps. (English summary)
J. Funct. Anal. 260 (2011), no. 5, 1476–1490.
46Lxx (47Axx 58Bxx)
2747767
Helton, J. William(1-UCSD); Klep, Igor(SV-LJUBMP); McCullough, Scott(1-FL)
Analytic mappings between noncommutative pencil balls. (English summary)
J. Math. Anal. Appl. 376 (2011), no. 2, 407–428.
47Axx (15A39 47Lxx)
2597682
Jury, Michael T.(1-FL); Knese, Greg(1-CA3); McCullough, Scott(1-FL)
Agler interpolation families of kernels. (English summary)
Oper. Matrices 3 (2009), no. 4, 571--587.
47A57 (46Exx 47A20 47Lxx)
2544753
Dym, Harry(IL-WEIZ); Greene, J. M.(1-UCSD); Helton, J. W.(1-UCSD); McCullough, S. A.(1-FL)
Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form. (English summary)
J. Anal. Math. 108 (2009), 19--59.
47Axx (16S36 16S38)
2500463
de Oliveira, Mauricio C.(1-UCSD-A); Helton, J. William(1-UCSD); McCullough, Scott A.(1-FL); Putinar, Mihai(1-UCSB)
Engineering systems and free semi-algebraic geometry. (English summary) Emerging applications of algebraic geometry, 17--61,
IMA Vol. Math. Appl., 149, Springer, New York, 2009.
93B25 (14P10)
2518108
Helton, J. William(1-UCSD); McCullough, Scott(1-FL); Putinar, Mihai(1-UCSB); Vinnikov, Victor(IL-BGUN)
Convex matrix inequalities versus linear matrix inequalities. (English summary)
IEEE Trans. Automat. Control 54 (2009), no. 5, 952--964.
90C25 (15A39 90C33)
2523335
Helton, J. William(1-UCSD); Klep, Igor(SV-LJUBMP); McCullough, Scott(1-FL); Slinglend, Nick(1-UCSD)
Noncommutative ball maps. (English summary)
J. Funct. Anal. 257 (2009), no. 1, 47--87.
47Axx (46Lxx 47Bxx 58Bxx)
2483003
Hay, Damon M.(1-NFL-MS); Helton, J. William(1-UCSD); Lim, Adrian(1-VDB); McCullough, Scott(1-FL)
Non-commutative partial matrix convexity. (English summary)
Indiana Univ. Math. J. 57 (2008), no. 6, 2815--2842.
47Axx (15Axx 16S36)
2389623
Dritschel, Michael A.(4-NWCT-SMS); McCullough, Scott(1-FL)
Test functions, kernels, realizations and interpolation. (English summary) Operator theory, structured matrices, and dilations, 153--179,
Theta Ser. Adv. Math., 7, Theta, Bucharest, 2007.
47A57 (46E22)
2358013
McCullough, Scott(1-FL); Sultanic, Saida(1-FL)
Ersatz commutant lifting with test functions. (English summary)
Complex Anal. Oper. Theory 1 (2007), no. 4, 581--620.
46E22
2346553
Dym, Harry(IL-WEIZ); Helton, J. William(1-UCSD); McCullough, Scott(1-FL)
The Hessian of a noncommutative polynomial has numerous negative eigenvalues. (English summary)
J. Anal. Math. 102 (2007), 29--76.
47A13
2337640
Dritschel, Michael A.(4-NWCT-SMS); Marcantognini, Stefania(YV-IVIC); McCullough, Scott(1-FL)
Interpolation in semigroupoid algebras. (English summary)
J. Reine Angew. Math. 606 (2007), 1--40.
47Axx (46E22 46Lxx 47Lxx)
2333470
Dym, Harry(IL-WEIZ); Helton, William(1-UCSD); McCullough, Scott(1-FL)
Irreducible noncommutative defining polynomials for convex sets have degree four or less. (English summary)
Indiana Univ. Math. J. 56 (2007), no. 3, 1189--1231.
16Sxx (47Axx)
2270289
Helton, J. William(1-UCSD); McCullough, Scott(1-FL); Putinar, Mihai(1-UCSB)
Strong majorization in a free $*$-algebra. (English summary)
Math. Z. 255 (2007), no. 3, 579--596.
46Axx (06F25 47Axx 47Bxx)
2259894
Helton, J. William(1-UCSD); McCullough, Scott A.(1-FL); Vinnikov, Victor(IL-BGUN)
Noncommutative convexity arises from linear matrix inequalities. (English summary)
J. Funct. Anal. 240 (2006), no. 1, 105--191.
15A39 (93B25)
2223591
Helton, J. William(1-UCSD); McCullough, Scott(1-FL); Putinar, Mihai(1-UCSB)
Matrix representations for positive noncommutative polynomials.
(English. English summary)
Positivity 10 (2006), no. 1, 145--163.
16S36
2224594
McCullough, Scott(1-FL); Putinar, Mihai(1-UCSB)
Noncommutative sums of squares.
(English. English summary)
Pacific J. Math. 218 (2005), no. 1, 167--171.
47Axx (46Lxx)
2179609
Helton, J. William(1-UCSD); McCullough, Scott A.(1-FL); Putinar, Mihai(1-UCSB)
Non-negative hereditary polynomials in a free $*$-algebra.
(English. English summary)
Math. Z. 250 (2005), no. 3, 515--522.
16S10
2163865
Dritschel, Michael A.(4-NWCT-SMS); McCullough, Scott(1-FL)
The failure of rational dilation on a triply connected domain.
J. Amer. Math. Soc. 18 (2005), no. 4, 873--918 (electronic).
47A20 (30C40 30E05 30H05 46E22 47A25 47A48)
2132691
Dritschel, Michael A.(4-NWCT-SMS); McCullough, Scott A.(1-FL)
Boundary representations for families of representations of operator algebras and spaces.
(English. English summary)
J. Operator Theory 53 (2005), no. 1, 159--167.
47Lxx (46Lxx 47Axx)
2081134
Helton, J. William(1-UCSD); McCullough, Scott(1-FL)
Convex noncommutative polynomials have degree two or less.
(English. English summary)
SIAM J. Matrix Anal. Appl. 25 (2004), no. 4, 1124--1139 (electronic).
47A63 (47A56)
2055751
Helton, J. William(1-UCSD); McCullough, Scott A.(1-FL)
A positivstellensatz for non-commutative polynomials.
(English. English summary)
Trans. Amer. Math. Soc. 356 (2004), no. 9, 3721--3737 (electronic).
47A13 (14Pxx)
2034923
Helton, J. William(1-UCSD); McCullough, Scott A.(1-FL); Putinar, Mihai(1-UCSB)
A non-commutative Positivstellensatz on isometries.
(English. English summary)
J. Reine Angew. Math. 568 (2004), 71--80.
47A13 (47A57)
2019960
McCullough, Scott(1-FL)
Extremal properties of outer polynomial factors.
(English. English summary)
Proc. Amer. Math. Soc. 132 (2004), no. 3, 815--825 (electronic).
47A68 (47A57)
1909298
McCullough, Scott(1-FL); Paulsen, Vern(1-HST)
$C\sp *$-envelopes and interpolation theory.
(English. English summary)
Indiana Univ. Math. J. 51 (2002), no. 2, 479--505.
46J15 (46L05 47A57 47L99)
1899491
McCullough, Scott(1-FL); Richter, Stefan(1-TN)
Bergman-type reproducing kernels, contractive divisors, and dilations.
(English. English summary)
J. Funct. Anal. 190 (2002), no. 2, 447--480.
47B32 (30C40 46E22 47A15)
1818066
McCullough, Scott(1-FL)
Isometric representations of some quotients of $H\sp \infty$ of an annulus.
(English. English summary)
Integral Equations Operator Theory 39 (2001), no. 3, 335--362.
46E25 (47B38)
1815959
McCullough, Scott(1-FL)
Factorization of operator-valued polynomials in several non-commuting variables.
(English. English summary)
Linear Algebra Appl. 326 (2001), no. 1-3, 193--203.
47A68 (47A13 47A20 47A56)
1800795
McCullough, Scott(1-FL); Trent, Tavan T.(1-AL)
Invariant subspaces and Nevanlinna-Pick kernels.
(English. English summary)
J. Funct. Anal. 178 (2000), no. 1, 226--249.
47A07 (42A82 46E22 47B32)
1741491
Dritschel, Michael A.(1-CINC); McCullough, Scott(1-FL)
Model theory for hyponormal contractions.
(English. English summary)
Integral Equations Operator Theory 36 (2000), no. 2, 182--192.
47A20 (47B20)
1707931
McCullough, Scott(1-FL)
Commutant lifting on a two holed domain.
(English. English summary)
Integral Equations Operator Theory 35 (1999), no. 1, 65--84.
47A20 (46E20 47B32)
1681577
Dritschel, Michael A.(1-PURD); McCullough, Scott(1-FL); Woerdeman, Hugo J.(1-CWM)
Model theory for $\rho$-contractions, $\rho\le2$.
(English. English summary)
J. Operator Theory 41 (1999), no. 2, 321--350.
47A45 (47A12 47A20 47A68)
1657163
McCullough, Scott A.(1-FL); Rodman, Leiba(1-CWM)
Normal generalized selfadjoint operators in Krein spaces.
(English. English summary)
Linear Algebra Appl. 283 (1998), no. 1-3, 239--245.
47B50
1473659
Clancy, Robert S.(1-FL); McCullough, Scott(1-FL)
Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel.
(English. English summary)
Proc. Amer. Math. Soc. 126 (1998), no. 11, 3299--3305.
47A20 (46E20 46H25 46J15 47A57 47B37)
1447975
McCullough, Scott A.(1-FL); Rodman, Leiba(1-CWM)
Hereditary classes of operators and matrices.
Amer. Math. Monthly 104 (1997), no. 5, 415--430.
47B20 (15A21 47A20)
1410590
McCullough, Scott A.(1-FL); Rodman, Leiba(1-CWM)
Two-selfadjoint operators in Kre\u\i n spaces.
(English. English summary)
Integral Equations Operator Theory 26 (1996), no. 2, 202--209.
47B50
1386331
McCullough, Scott(1-FL)
The trisecant identity and operator theory.
(English. English summary)
Integral Equations Operator Theory 25 (1996), no. 1, 104--127.
46E22 (30C40 30D55 47B38)
1367626
McCullough, Scott(1-FL)
Nevanlinna-Pick type interpolation in a dual algebra.
(English. English summary)
J. Funct. Anal. 135 (1996), no. 1, 93--131.
47A57 (30D50 30E05 46E22 46J15 47D27)
1352602
McCullough, Scott(1-FL)
Matrix functions of positive real part on an annulus.
(English. English summary)
Houston J. Math. 21 (1995), no. 3, 489--506.
47A20 (30E10)
1287987
Mair, B. A.(1-FL); McCullough, Scott(1-FL)
Invariance of extreme harmonic functions on an annulus; applications to theta functions.
Houston J. Math. 20 (1994), no. 3, 453--473.
33D10 (31A05)
1284929
McCullough, Scott(1-FL)
The local de Branges-Rovnyak construction and complete Nevanlinna-Pick kernels.
Algebraic methods in operator theory,
15--24,
Birkhäuser Boston, Boston, MA, 1994.
47A57 (30C40 30E05 46E22)
1189748
McCullough, Scott(1-FL); Shen, Li-Chien(1-FL)
On the Szegö kernel of an annulus.
(English. English summary)
Proc. Amer. Math. Soc. 121 (1994), no. 4, 1111--1121.
30C40 (46E22)
1226443
Mair, B. A.(1-FL); McCullough, Scott(1-FL); Rao, Murali(1-FL)
Wavelets generated by three-term two-scale relations.
(English. English summary)
Ulam Quart. 2 (1993), no. 1, 24ff., approx. 8 pp. (electronic only).
42C15 (41A15)
1209391
McCullough, Scott(1-FL)
Minimal separators of $2$-chordal graphs.
(English. English summary)
Linear Algebra Appl. 184 (1993), 187--199.
05C75
1134687
McCullough, Scott(1-FL)
Carathéodory interpolation kernels.
Integral Equations Operator Theory 15 (1992), no. 1, 43--71.
47A57
1102858
McCullough, Scott(1-FL); Paulsen, Vern(1-HST)
$k$-hyponormality of weighted shifts.
Proc. Amer. Math. Soc. 116 (1992), no. 1, 165--169.
47B20 (47B37)
1043729
McCullough, Scott(1-IN)
Sub-Brownian operators.
J. Operator Theory 22 (1989), no. 2, 291--305.
47B20 (47A20)
972236
McCullough, Scott(1-IN); Paulsen, Vern(1-HST)
A note on joint hyponormality.
Proc. Amer. Math. Soc. 107 (1989), no. 1, 187--195.
47B20
1017669
McCullough, Scott(1-IN)
$2$-chordal graphs.
Contributions to operator theory and its applications (Mesa, AZ, 1987),
143--192,
Oper. Theory Adv. Appl., 35,
Birkhäuser, Basel, 1988.
05C50 (15A99)
960140
Agler, Jim(1-UCSD); Helton, J. William(1-UCSD); McCullough, Scott(1-UCSD); Rodman, Leiba(IL-TLAV)
Positive semidefinite matrices with a given sparsity pattern.
Proceedings of the Victoria Conference on Combinatorial Matrix Analysis (Victoria, BC, 1987).
Linear Algebra Appl. 107 (1988), 101--149.
15A48
792284
McCullough, Scott(1-UCSD); Wulbert, Daniel(1-UCSD)
The topological spaces that support Haar systems.
Proc. Amer. Math. Soc. 94 (1985), no. 4, 687--692.
41A52 (41A45 41A65)
Last update made
Thu Mar 21 14:01:58 EDT 2019