Non-Commutative Spectral Theory for Affine Function Spaces on Convex Sets PDF Download
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Author: Erik Magnus Alfsen
Publisher: American Mathematical Soc.
ISBN: 0821818724
Category : C*-algebras
Languages : en
Pages : 136
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Book Description
In this paper we develop geometric notions related to self-adjoint projections and one-sided ideals in operator algebras. In the context of affine function spaces on convex sets we define projective units. P-projections, and projective faces which generalize respectively self-adjoint projections p, the maps a [right arrow] pap, and closed faces of state spaces of operator algebras. In terms of these concepts we state a "spectral axiom" requiring the existence of "sufficiently many" projective objects. We then prove the spectral theorem: that elements of the affine function space admit a unique spectral decomposition. This in turn yields a satisfactory functional calculus, which is unique under a natural minimality requirement (that it be "extreme point preserving").
Author: Erik Magnus Alfsen
Publisher: American Mathematical Soc.
ISBN: 0821818724
Category : C*-algebras
Languages : en
Pages : 136
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Book Description
In this paper we develop geometric notions related to self-adjoint projections and one-sided ideals in operator algebras. In the context of affine function spaces on convex sets we define projective units. P-projections, and projective faces which generalize respectively self-adjoint projections p, the maps a [right arrow] pap, and closed faces of state spaces of operator algebras. In terms of these concepts we state a "spectral axiom" requiring the existence of "sufficiently many" projective objects. We then prove the spectral theorem: that elements of the affine function space admit a unique spectral decomposition. This in turn yields a satisfactory functional calculus, which is unique under a natural minimality requirement (that it be "extreme point preserving").
Author: Bronius Grigelionis
Publisher: VSP
ISBN: 9789067641289
Category : Mathematical statistics
Languages : en
Pages : 656
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Book Description
Author: B. Grigelionis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112314190
Category : Mathematics
Languages : en
Pages : 656
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Book Description
No detailed description available for "GRIGELIONIS: PROCEEDINGS OF THE FIFTH VILNIUS CONFERE E-BOOK".
Author: L. Asimow
Publisher: Elsevier
ISBN: 1483294692
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Convexity Theory Appl Functional Analysis
Author: Erik M. Alfsen
Publisher: Springer Science & Business Media
ISBN: 1461200199
Category : Mathematics
Languages : en
Pages : 470
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Book Description
In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.
Author: Erik M. Alfsen
Publisher: Springer Science & Business Media
ISBN: 1461201470
Category : Mathematics
Languages : en
Pages : 362
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Book Description
The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.
Author: Harald Upmeier
Publisher: American Mathematical Soc.
ISBN: 9780821889121
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Author: K.-D. Bierstedt
Publisher: Elsevier
ISBN: 0080871496
Category : Mathematics
Languages : en
Pages : 355
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Book Description
Functional Analysis: Surveys and Recent Results II
Author: Charles A. Akemann
Publisher: American Mathematical Soc.
ISBN: 0821823272
Category : Mathematics
Languages : en
Pages : 137
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Book Description
This monograph investigates [italic]C*-algebras.
Author: B. Grigelionis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311231932X
Category : Mathematics
Languages : en
Pages : 752
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Book Description
No detailed description available for "Probability Theory and Mathematical Statistics".
