Unitary invariants in multivariable operator theory
Author(s)
Bibliographic Information
Unitary invariants in multivariable operator theory
（Memoirs of the American Mathematical Society, no. 941）
American Mathematical Society, 2009
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"Volume 200, Number 941 (end of volume)"
Includes bibliographical references (p. 89-91)
Description and Table of Contents
Description
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.
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