ENGLISH

Unitary invariants in multivariable operator theory

By Gelu Popescu

Book information

Publisher
Amer Mathematical Society
Year
2009
ISBN
0821843966, 978-0-8218-4396-3
Language
english
Format
PDF
Filesize
1 MB (1202795 bytes)
Series
Memoirs of the American Mathematical Society 0941
Pages
105\105
Library
kolxoz
Time added
2015-12-12 14:00:00

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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