Multivariable Operator Theory
Multivariable Operator Theory

Author: Ernst Albrecht

Publisher: Springer Nature

Published: 2024-01-22

Total Pages: 893

ISBN-13: 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.

Foundations of Free Noncommutative Function Theory
Foundations of Free Noncommutative Function Theory

Author: Dmitry S. Kaliuzhnyi-Verbovetskyi

Publisher: American Mathematical Soc.

Published: 2014-11-19

Total Pages: 194

ISBN-13: 1470416972

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In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

Small Modifications of Quadrature Domains
Small Modifications of Quadrature Domains

Author: Makoto Sakai

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 282

ISBN-13: 0821848100

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For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.

Crossed Products of Operator Algebras
Crossed Products of Operator Algebras

Author: Elias G. Katsoulis

Publisher: American Mathematical Soc.

Published: 2019-04-10

Total Pages: 100

ISBN-13: 1470435454

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The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates
Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates

Author: Steve Hofmann

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 91

ISBN-13: 0821852388

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Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.

Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case
Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case

Author: Martin C. Olsson

Publisher: American Mathematical Soc.

Published: 2011-02-07

Total Pages: 170

ISBN-13: 082185240X

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The author develops a non-abelian version of $p$-adic Hodge Theory for varieties (possibly open with ``nice compactification'') with good reduction. This theory yields in particular a comparison between smooth $p$-adic sheaves and $F$-isocrystals on the level of certain Tannakian categories, $p$-adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups.