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Unitary Invariants in Multivariable Operator Theory
 
Gelu Popescu University of Texas at San Antonio, San Antonio, TX
Unitary Invariants in Multivariable Operator Theory
eBook ISBN:  978-1-4704-0555-7
Product Code:  MEMO/200/941.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
Unitary Invariants in Multivariable Operator Theory
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Unitary Invariants in Multivariable Operator Theory
Gelu Popescu University of Texas at San Antonio, San Antonio, TX
eBook ISBN:  978-1-4704-0555-7
Product Code:  MEMO/200/941.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2002009; 91 pp
    MSC: Primary 47;

    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 \(F_n^\infty\).

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Unitary invariants for $n$-tuples of operators
    • Chapter 2. Joint operator radii, inequalities, and applications
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2002009; 91 pp
MSC: Primary 47;

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 \(F_n^\infty\).

  • Chapters
  • Introduction
  • Chapter 1. Unitary invariants for $n$-tuples of operators
  • Chapter 2. Joint operator radii, inequalities, and applications
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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