Unitary Invariants In Multivariable Operator Theory

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Unitary Invariants in Multivariable Operator Theory

Gelu Popescu
Unitary Invariants in Multivariable Operator Theory Book PDF

Author : Gelu Popescu
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 49,5 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843963

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Unitary Invariants in Multivariable Operator Theory by Gelu Popescu Pdf

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

Raúl E. Curto
Multivariable Operator Theory Book PDF

Author : Raúl E. Curto
Publisher : American Mathematical Soc.
Page : 380 pages
File Size : 54,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802984

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Multivariable Operator Theory by Raúl E. Curto Pdf

This volume contains a collection of papers presented at the Summer Research Conference on Multivariable Operator Theory, held in July 1993 at the University of Washington in Seattle. 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. Developments have occurred in several different directions, with the aid of a variety of techniques, and many advances have been made through cross-pollination among different areas of mathematics. The goal of the conference, and of this volume, is to spur discussion of the connections among the various approaches and new directions for research.

Multivariable Operator Theory

Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Multivariable Operator Theory Book PDF

Author : Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar
Publisher : Springer Nature
Page : 893 pages
File Size : 47,7 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9783031505355

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Multivariable Operator Theory by Ernst Albrecht,Raúl Curto,Michael Hartz,Mihai Putinar Pdf

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.

Operator Theory on Noncommutative Domains

Gelu Popescu
Operator Theory on Noncommutative Domains Book PDF

Author : Gelu Popescu
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 54,7 Mb
Release : 2010
Category : Dilation theory (Operator theory).
ISBN : 9780821847107

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Operator Theory on Noncommutative Domains by Gelu Popescu Pdf

"Volume 205, number 964 (third of 5 numbers)."

Operator Algebras for Multivariable Dynamics

Kenneth R. Davidson,Elias G. Katsoulis
Operator Algebras for Multivariable Dynamics Book PDF

Author : Kenneth R. Davidson,Elias G. Katsoulis
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 41,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853023

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Operator Algebras for Multivariable Dynamics by Kenneth R. Davidson,Elias G. Katsoulis Pdf

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.

Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space

Zeng Lian,Kening Lu
Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space Book PDF

Author : Zeng Lian,Kening Lu
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 42,5 Mb
Release : 2010
Category : Banach spaces
ISBN : 9780821846568

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Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space by Zeng Lian,Kening Lu Pdf

The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.

Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory

Marius Junge,Javier Parcet
Mixed Norm Inequalities and Operator Space L p Embedding Theory Book PDF

Author : Marius Junge,Javier Parcet
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 52,7 Mb
Release : 2010
Category : Banach spaces
ISBN : 9780821846551

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Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory by Marius Junge,Javier Parcet Pdf

Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.

Cohomological Invariants: Exceptional Groups and Spin Groups

Skip Garibaldi
Cohomological Invariants Exceptional Groups and Spin Groups Book PDF

Author : Skip Garibaldi
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 50,6 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821844045

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Cohomological Invariants: Exceptional Groups and Spin Groups by Skip Garibaldi Pdf

This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.

Harmonic Analysis of Operators on Hilbert Space

Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy
Harmonic Analysis of Operators on Hilbert Space Book PDF

Author : Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 54,6 Mb
Release : 2010-09-01
Category : Mathematics
ISBN : 9781441960931

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Harmonic Analysis of Operators on Hilbert Space by Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy Pdf

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

Pascal Lefèvre
Composition Operators on Hardy Orlicz Spaces Book PDF

Author : Pascal Lefèvre
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 50,5 Mb
Release : 2010
Category : Composition operators
ISBN : 9780821846377

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Composition Operators on Hardy-Orlicz Spaces by Pascal Lefèvre Pdf

"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.

Definable Additive Categories: Purity and Model Theory

Mike Prest
Definable Additive Categories Purity and Model Theory Book PDF

Author : Mike Prest
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 54,6 Mb
Release : 2011-02-07
Category : Mathematics
ISBN : 9780821847671

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Definable Additive Categories: Purity and Model Theory by Mike Prest Pdf

Most of the model theory of modules works, with only minor modifications, in much more general additive contexts (such as functor categories, categories of comodules, categories of sheaves). Furthermore, even within a given category of modules, many subcategories form a ``self-sufficient'' context in which the model theory may be developed without reference to the larger category of modules. The notion of a definable additive category covers all these contexts. The (imaginaries) language which one uses for model theory in a definable additive category can be obtained from the category (of structures and homomorphisms) itself, namely, as the category of those functors to the category of abelian groups which commute with products and direct limits. Dually, the objects of the definable category--the modules (or functors, or comodules, or sheaves)--to which that model theory applies may be recovered as the exact functors from the, small abelian, category (the category of pp-imaginaries) which underlies that language.

Iwasawa Theory, Projective Modules, and Modular Representations

Ralph Greenberg
Iwasawa Theory Projective Modules and Modular Representations Book PDF

Author : Ralph Greenberg
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 40,7 Mb
Release : 2010
Category : Curves, Elliptic
ISBN : 9780821849316

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Iwasawa Theory, Projective Modules, and Modular Representations by Ralph Greenberg Pdf

This paper shows that properties of projective modules over a group ring $\mathbf{Z}_p[\Delta]$, where $\Delta$ is a finite Galois group, can be used to study the behavior of certain invariants which occur naturally in Iwasawa theory for an elliptic curve $E$. Modular representation theory for the group $\Delta$ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a $\mu$-invariant. The author then studies $\lambda$-invariants $\lambda_E(\sigma)$, where $\sigma$ varies over the absolutely irreducible representations of $\Delta$. He shows that there are non-trivial relationships between these invariants under certain hypotheses.

Banach Algebras on Semigroups and on Their Compactifications

Harold G. Dales,Anthony To-Ming Lau,Dona Strauss
Banach Algebras on Semigroups and on Their Compactifications Book PDF

Author : Harold G. Dales,Anthony To-Ming Lau,Dona Strauss
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 48,9 Mb
Release : 2010
Category : Banach algebras
ISBN : 9780821847756

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Banach Algebras on Semigroups and on Their Compactifications by Harold G. Dales,Anthony To-Ming Lau,Dona Strauss Pdf

"Volume 205, number 966 (end of volume)."

Approximate Homotopy of Homomorphisms from C(X) Into a Simple C*-algebra

Huaxin Lin
Approximate Homotopy of Homomorphisms from C X Into a Simple C algebra Book PDF

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 53,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851944

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Approximate Homotopy of Homomorphisms from C(X) Into a Simple C*-algebra by Huaxin Lin Pdf

In this paper the author proves Generalized Homotopy Lemmas. These type of results play an important role in the classification theory of $*$-homomorphisms up to asymptotic unitary equivalence. Table of Contents: Prelude; The basic homotopy lemma for higher dimensional spaces; Purely infinite simple $C^*$-algebras; Approximate homotopy; Super homotopy; Postlude; Bibliography. (MEMO/205/963)