Continuous Tensor Products And Arveson S Spectral C Algebras
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Continuous Tensor Products And Arveson S Spectral C Algebras
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Author : Joachim Zacharias
language : en
Publisher:
Release Date : 2000
Continuous Tensor Products And Arveson S Spectral C Algebras written by Joachim Zacharias and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with C*-algebras categories.
Continuous Tensor Products And Arveson S Spectral C Algebras
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Author : Joachim Zacharias
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Continuous Tensor Products And Arveson S Spectral C Algebras written by Joachim Zacharias and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in operator algebras
Continuous Tensor Products And Arveson S Spectral C Algebras
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Author : Joachim Zacharias
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-12-29
Continuous Tensor Products And Arveson S Spectral C Algebras written by Joachim Zacharias and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-29 with Mathematics categories.
Advances In Quantum Dynamics
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Author : Geoffrey L. Price
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Advances In Quantum Dynamics written by Geoffrey L. Price and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversiblesystems, also called dissipative systems. The time parameter is the half-line, and the transformations are now endomorphisms as opposed to automorphisms. For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such asBrownian motion, dilation theory, quantum probability, and free probability. The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.
Splitting Theorems For Certain Equivariant Spectra
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Author : L. Gaunce Lewis
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Splitting Theorems For Certain Equivariant Spectra written by L. Gaunce Lewis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in algebraic topology.
Non Additive Exact Functors And Tensor Induction For Mackey Functors
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Author : Serge Bouc
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Non Additive Exact Functors And Tensor Induction For Mackey Functors written by Serge Bouc and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
First the author introduces a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category. Next those results are used to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for p-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.
Equivariant E Theory For C Algebras
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Author : Erik Guentner
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Equivariant E Theory For C Algebras written by Erik Guentner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
On Natural Coalgebra Decompositions Of Tensor Algebras And Loop Suspensions
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Author : Paul Selick
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
On Natural Coalgebra Decompositions Of Tensor Algebras And Loop Suspensions written by Paul Selick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in topology and representation theory.
Categories Of Operator Modules Morita Equivalence And Projective Modules
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Author : David P. Blecher
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Categories Of Operator Modules Morita Equivalence And Projective Modules written by David P. Blecher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
We employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and pairings (\cdot,\cdot) and [\cdot,\cdot] that induce (complete) isomorphisms betweenthe (balanced) Haagerup tensor products, X \otimes {hB} {} Y and Y \otimes {hA} {} X, and the algebras, A and B, respectively. Thus, formally, a Morita context is the same as that which appears in pure ring theory. The subtleties of the theory lie in the interplay between the pure algebra and the operator space geometry. Our analysis leads to viable notions of projective operator modules and dual operator modules. We show that two C*-algebras are Morita equivalent in our sense if and only ifthey are C*-algebraically strong Morita equivalent, and moreover the equivalence bimodules are the same. The distinctive features of the non-self-adjoint theory are illuminated through a number of examples drawn from complex analysis and the theory of incidence algebras over topological partial orders.Finally, an appendix provides links to the literature that developed since this Memoir was accepted for publication.
Multi Interval Linear Ordinary Boundary Value Problems And Complex Symplectic Algebra
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Author : William Norrie Everitt
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Multi Interval Linear Ordinary Boundary Value Problems And Complex Symplectic Algebra written by William Norrie Everitt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
A multi-interval quasi-differential system $\{I_{r},M_{r},w_{r}:r\in\Omega\}$ consists of a collection of real intervals, $\{I_{r}\}$, as indexed by a finite, or possibly infinite index set $\Omega$ (where $\mathrm{card} (\Omega)\geq\aleph_{0}$ is permissible), on which are assigned ordinary or quasi-differential expressions $M_{r}$ generating unbounded operators in the Hilbert function spaces $L_{r}^{2}\equiv L^{2}(I_{r};w_{r})$, where $w_{r}$ are given, non-negative weight functions. For each fixed $r\in\Omega$ assume that $M_{r}$ is Lagrange symmetric (formally self-adjoint) on $I_{r}$ and hence specifies minimal and maximal closed operators $T_{0,r}$ and $T_{1,r}$, respectively, in $L_{r}^{2}$. However the theory does not require that the corresponding deficiency indices $d_{r}^{-}$ and $d_{r}^{+}$ of $T_{0,r}$ are equal (e. g. the symplectic excess $Ex_{r}=d_{r}^{+}-d_{r}^{-}\neq 0$), in which case there will not exist any self-adjoint extensions of $T_{0,r}$ in $L_{r}^{2}$. In this paper a system Hilbert space $\mathbf{H}:=\sum_{r\,\in\,\Omega}\oplus L_{r}^{2}$ is defined (even for non-countable $\Omega$) with corresponding minimal and maximal system operators $\mathbf{T}_{0}$ and $\mathbf{T}_{1}$ in $\mathbf{H}$. Then the system deficiency indices $\mathbf{d}^{\pm} =\sum_{r\,\in\,\Omega}d_{r}^{\pm}$ are equal (system symplectic excess $Ex=0$), if and only if there exist self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$ in $\mathbf{H}$. The existence is shown of a natural bijective correspondence between the set of all such self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$, and the set of all complete Lagrangian subspaces $\mathsf{L}$ of the system boundary complex symplectic space $\mathsf{S}=\mathbf{D(T}_{1})/\mathbf{D(T}_{0})$. This result generalizes the earlier symplectic version of the celebrated GKN-Theorem for single interval systems to multi-interval systems. Examples of such complete Lagrangians, for both finite and infinite dimensional complex symplectic $\mathsf{S}$, illuminate new phenoma for the boundary value problems of multi-interval systems. These concepts have applications to many-particle systems of quantum mechanics, and to other physical problems.