Non-associative normed algebras.: Volume 1, The Vidav-Palmer and Gelfand-Naimark theorems
(eBook)
Author:
Contributors:
Rodriguez Palacios, Ángel, author.
Series:
Published:
Cambridge : Cambridge University Press, 2014.
Format:
eBook
ISBN:
9781316006566, 1316006565, 9781107337763, 1107337763, 9781316004302, 1316004309, 9781139990455, 1139990454, 9781316002063, 1316002063, 9781322066707, 1322066701, 1316011062, 9781316011065, 1139985833, 9781139985833, 1316013308, 9781316013304, 1316008800, 9781316008805
Physical Desc:
1 online resource (xxii, 712 pages)
Status:
Ebsco (CCU)
Description
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.
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APA Citation (style guide)
Cabrera García, M., & Rodriguez Palacios, A. (2014). Non-associative normed algebras. Cambridge, Cambridge University Press.
Chicago / Turabian - Author Date Citation (style guide)Cabrera García, Miguel and Ángel, Rodriguez Palacios. 2014. Non-associative Normed Algebras. Cambridge, Cambridge University Press.
Chicago / Turabian - Humanities Citation (style guide)Cabrera García, Miguel and Ángel, Rodriguez Palacios, Non-associative Normed Algebras. Cambridge, Cambridge University Press, 2014.
MLA Citation (style guide)Cabrera García, Miguel, and Ángel Rodriguez Palacios. Non-associative Normed Algebras. Cambridge, Cambridge University Press, 2014.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English
Notes
Bibliography
Includes bibliographical references (pages 671-703) and indexes.
Description
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.
Language
English.
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Grouped Work ID:
981eea43-24d4-5626-6a5b-03d4076881c1
Record Information
| Last File Modification Time | Apr 05, 2024 09:36:26 PM |
|---|---|
| Last Grouped Work Modification Time | Apr 05, 2024 09:12:39 PM |
MARC Record
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| 100 | 1 | |a Cabrera García, Miguel,|e author. | |
| 245 | 1 | 0 | |a Non-associative normed algebras.|n Volume 1,|p The Vidav-Palmer and Gelfand-Naimark theorems /|c Miguel Cabrera García, Universidad de Granada, Ángel Rodriguez Palacios, Universidad de Granada. |
| 246 | 3 | 0 | |a Vidav-Palmer and Gelfand-Naimark theorems |
| 264 | 1 | |a Cambridge :|b Cambridge University Press,|c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xxii, 712 pages) | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ;|v 154 | |
| 504 | |a Includes bibliographical references (pages 671-703) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography. | ||
| 505 | 0 | |a Cover; Half-title ; Series information; Title page ; Copyright information; Dedication; Table of contents; Preface; 1 Foundations; 1.1 Rudiments on normed algebras; 1.1.1 Basic spectral theory; 1.1.2 Rickart's dense-range-homomorphism theorem; 1.1.3 Gelfand's theory; 1.1.4 Topological divisors of zero; 1.1.5 The complexification of a normed real algebra; 1.1.6 The unital extension and the completion of a normed algebra; 1.1.7 Historical notes and comments; 1.2 Introducing C*-algebras; 1.2.1 The results; 1.2.2 Historical notes and comments; 1.3 The holomorphic functional calculus | |
| 505 | 8 | |a 1.3.1 The polynomial and rational functional calculuses1.3.2 The main results; 1.3.3 Historical notes and comments; 1.4 Compact and weakly compact operators; 1.4.1 Operators from a normed space to another; 1.4.2 Operators from a normed space to itself; 1.4.3 Discussing the inclusion [overline(mathfrak F (X, Y))] subseteq mathfrak K (X, Y) in the non-complete setting; 1.4.4 Historical notes and comments; 2 Beginning the proof of the non-associative Vidav-Palmer theorem; 2.1 Basic results on numerical ranges; 2.1.1 Algebra numerical ranges; 2.1.2 Operator numerical ranges | |
| 505 | 8 | |a 2.1.3 Historical notes and comments2.2 An application to Kadison's isometry theorem; 2.2.1 Non-associative results; 2.2.2 The Kadison-Paterson-Sinclair theorem; 2.2.3 Historical notes and comments; 2.3 The associative Vidav-Palmer theorem, starting from a non-associative germ; 2.3.1 Natural involutions of V-algebras are algebra involutions; 2.3.2 The associative Vidav-Palmer theorem; 2.3.3 Complements on C*-algebras; 2.3.4 Introducing alternative C*-algebras; 2.3.5 Historical notes and comments; 2.4 V-algebras are non-commutative Jordan algebras; 2.4.1 The main result | |
| 505 | 8 | |a 2.4.2 Applications to C*-algebras2.4.3 Historical notes and comments; 2.5 The Frobenius-Zorn theorem, and the generalized Gelfand-Mazur-Kaplansky theorem; 2.5.1 Introducing quaternions and octonions; 2.5.2 The Frobenius-Zorn theorem; 2.5.3 The generalized Gelfand-Mazur-Kaplansky theorem; 2.5.4 Historical notes and comments; 2.6 Smooth-normed algebras, and absolute-valued unital algebras; 2.6.1 Determining smooth-normed algebras and absolute-valued unital algebras; 2.6.2 Unit-free characterizations of smooth-normed algebras, and of absolute-valued unital algebras | |
| 505 | 8 | |a 2.6.3 Historical notes and comments2.7 Other Gelfand-Mazur type non-associative theorems; 2.7.1 Focusing on complex algebras; 2.7.2 Involving real scalars; 2.7.3 Discussing the results; 2.7.4 Historical notes and comments; 2.8 Complements on absolute-valued algebras and algebraicity; 2.8.1 Continuity of algebra homomorphisms into absolute-valued algebras; 2.8.2 Absolute values on H*-algebras; 2.8.3 Free non-associative algebras are absolute-valued algebras; 2.8.4 Complete normed algebraic algebras are of bounded degree; 2.8.5 Absolute-valued algebraic algebras are finite-dimensional | |
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