Unitary Invariants in Multivariable Operator Theory

By Gelu Popescu. 2004

127 citations recorded by the source corpus.

This paper concerns unitary invariants for n-tuples T:=(Tl,...,Tn) of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger - Kato - Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of T in connection with several unitary invariants for n-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra Fn.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/155b374b636aba8d128e4c04a06ee226e7e9c583

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Operator Theory on Noncommutative Domains (2007, unknown): “, Yn] is a row contraction and curvp1(T ) = curv(Y ), where curv(Y ) is the curvature associated with a row contraction Y (see [86]).”
Operator theory on noncommutative varieties (2005, background): “The theory is based on a class of constrained Poisson kernels (see [30], [1], [35], and [6] for n = 1) associated with T := [T1, .”
Free holomorphic functions on the unit ball of B(H)n (2006, methodology): “We refer to [35,36,44] for more on noncommutative Poisson transforms on C∗-algebras generated by isometries.”
Extension of Euclidean operator radius inequalities (2015, background): “× B(H ) was defined in [9] by we(T1, .”