Unitary Invariants in Multivariable Operator Theory

Unitary Invariants in Multivariable Operator Theory
Author: Gelu Popescu
Publisher: American Mathematical Soc.
Total Pages: 105
Release: 2009-06-05
Genre: Mathematics
ISBN: 0821843966
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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 $F_n^\infty$.

Multivariable Operator Theory

Multivariable Operator Theory
Author: Raúl E. Curto
Publisher: American Mathematical Soc.
Total Pages: 396
Release: 1995
Genre: Mathematics
ISBN: 0821802984
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This is a collection of papers presented at a conference on multivariable operator theory. The articles contain contributions to a variety of areas and topics which may be viewed as forming an emerging new subject. This subject involves the study of geometric rather than topological invariants associated with the general theme of operator theory in several variables. This collection will spur further discussion among the different research groups.

Multivariable Operator Theory

Multivariable Operator Theory
Author: Ernst Albrecht
Publisher: Springer Nature
Total Pages: 893
Release: 2024-01-22
Genre: Mathematics
ISBN: 3031505352
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Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Harmonic Analysis of Operators on Hilbert Space

Harmonic Analysis of Operators on Hilbert Space
Author: Béla Sz Nagy
Publisher: Springer Science & Business Media
Total Pages: 481
Release: 2010-09-01
Genre: Mathematics
ISBN: 1441960937
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The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

Composition Operators on Hardy-Orlicz Spaces

Composition Operators on Hardy-Orlicz Spaces
Author: Pascal Lefèvre
Publisher: American Mathematical Soc.
Total Pages: 87
Release: 2010
Genre: Mathematics
ISBN: 082184637X
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"The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Psi grows rapidly: compactness, weak compactness, to be p-summing, order bounded, ... , and show how these notions behave according to the growth of Psi. They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces."--Publisher's description.