# Unitary Invariants in Multivariable Operator Theory

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This paper concerns unitary invariants for $n$-tuples $T:=(T_1, \ldots, T_n)$ 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 $F_n^\infty$.The AMS Author Handbook and the Instruction Manual are available in PDF format from the author package link. ... sent via FTP, or sent on CD-Rom or diskette to the Electronic Prepress Department, American Mathematical Society, 201anbsp;...

 Title : Unitary Invariants in Multivariable Operator Theory Author : Gelu Popescu Publisher : American Mathematical Soc. - 2009-06-05