Stereotype Spaces and Algebras
Stereotype Spaces and Algebras

Author: Sergei S. Akbarov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-08-22

Total Pages: 871

ISBN-13: 3110780968

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The term “stereotype space” was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this fi eld closer to other main branches of mathematics, namely, to algebra and geometry. This volume contains the foundations of the theory of stereotype spaces, with accurate definitions, formulations, proofs, and numerous examples illustrating the interaction of this discipline with the category theory, the theory of Hopf algebras, and the four big geometric disciplines: topology, differential geometry, complex geometry, and algebraic geometry.

Topological Algebras with Involution
Topological Algebras with Involution

Author: M. Fragoulopoulou

Publisher: Elsevier

Published: 2005-07-26

Total Pages: 514

ISBN-13: 0080461220

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This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.Key features:- Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers.- Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.

Integral Representation
Integral Representation

Author: Walter Roth

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-10-04

Total Pages: 266

ISBN-13: 3111315479

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This book presents a wide-ranging approach to operator-valued measures and integrals of both vector-valued and set-valued functions. It covers convergence theorems and an integral representation for linear operators on spaces of continuous vector-valued functions on a locally compact space. These are used to extend Choquet theory, which was originally formulated for linear functionals on spaces of real-valued functions, to operators of this type.

The d-bar Neumann Problem and Schrödinger Operators
The d-bar Neumann Problem and Schrödinger Operators

Author: Friedrich Haslinger

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-09-18

Total Pages: 336

ISBN-13: 3111182924

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This book's subject lies in the nexus of partial differential equations, operator theory, and complex analysis. The spectral analysis of the complex Laplacian and the compactness of the d-bar-Neumann operator are primary topics.The revised 2nd edition explores updates to Schrödinger operators with magnetic fields and connections to the Segal Bargmann space (Fock space), to quantum mechanics, and the uncertainty principle.

Topological Homology
Topological Homology

Author:

Publisher: Nova Biomedical Books

Published: 2000

Total Pages: 230

ISBN-13:

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Contains some results obtained during seminars over the last few years. The seven papers discuss stereotype spaces, algebras and homologies; flat operator modules and their dual modules; homological dimensions of C*- algebras; Wedderburn-type theorems for operator algebras and modules; injective topological modules and additivity formulas for homological dimensions; coretraction problems and homological properties of Banach algebras; and the Sobolev algebra and indecomposable spatially projective operator algebras.

Linear Algebra and Analytic Geometry
Linear Algebra and Analytic Geometry

Author: Bennie Marsh & Frankie Murray

Publisher: Scientific e-Resources

Published: 2018-01-18

Total Pages: 293

ISBN-13: 1839473185

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In this book, the topics are presented in the same order as in the textbook. The problems concern two content areas: Linear Algebra, and Analytical Geometry. After reading this book, a student should be ables to solve linear equations and to perform the basic operations on numbers and algebraic expressions. The Linear Algebra tests will reveal readers' knowledge and skills, readers' abilities in interpreting symbols, justifying statements and constructing proofs. Readers should be able to apply the properties of determinants and matrix operations and solve linear systems of equations. The Analytical Geometry topics include different forms of equations of straight lines and planes; angles between simple figures; the curves of the second order. This book will prove definitive and ideal reference tool to research scholars, academicians and educationists.