Unitary Invariants in Multivariable Operator Theory

Released on by Gelu Popescu
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  • Unitary Invariants in Multivariable Operator Theory Book Detail

  • Author : Gelu Popescu
  • Release Date : 2009-06-05
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 105
  • ISBN 13 : 0821843966
  • File Size : 26,26 MB
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Unitary Invariants in Multivariable Operator Theory by Gelu Popescu PDF Summary

Book Description: 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 $F_n^\infty$.

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