A note on values of noncommutative polynomials

DOI10.1090/S0002-9939-10-10324-4zbMath1213.47068arXiv0909.2640OpenAlexW3105263125MaRDI QIDQ3574811

Igor Klep, Matej Brešar

Publication date: 2 July 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.2640

zbMATH Keywords

Hilbert spacecompact operatornoncommutative polynomialbounded operatorLie ideal

Mathematics Subject Classification ID

Abstract operator algebras on Hilbert spaces (47L30) Free algebras (08B20) Rings with polynomial identity (16R99)

Related Items (8)

Additive subgroups generated by noncommutative polynomials ⋮ Values of polynomials on centrally closed prime algebras ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ The images of multilinear and semihomogeneous polynomials on the algebra of octonions ⋮ Non-commutative polynomial solutions to partial differential equations ⋮ On the images of generalized polynomials evaluated on matrices over an algebraically closed skew field ⋮ Commutators and images of noncommutative polynomials ⋮ NON-COMMUTATIVE REPRESENTATIONS OF FAMILIES OF k² COMMUTATIVE POLYNOMIALS IN 2k² COMMUTING VARIABLES

Cites Work

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• Values of noncommutative polynomials, Lie skew-ideals and tracial Nullstellensätze.
• ``Positive noncommutative polynomials are sums of squares.
• Connes' embedding conjecture and sums of Hermitian squares
• On commutators in ideals of compact operators
• Lie ideals: from pure algebra to C*-algebras
• Commutators of compact operators.
• Commutators of Operators, II

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