Unitary Invariants in Multivariable Operator Theory (Memoirs of the American Mathematical Society)

Unitary Invariants in Multivariable Operator Theory (Memoirs of the American Mathematical Society)

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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.

Product Details

  • ISBN13: 9780821843963
  • Format: Paperback
  • Number Of Pages: 91
  • ID: 9780821843963
  • ISBN10: 0821843966

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