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Quantum functional analysis : = non-...

Khelemskii, A. Ia.(Aleksandr IAkovlevich)

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Quantum functional analysis : = non-coordinate approach /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Quantum functional analysis :/ A. Ya. Helemskii.
Reminder of title:	non-coordinate approach /
Author:	Khelemskii, A. Ia.(Aleksandr IAkovlevich)
Published:	Providence, R.I. :American Mathematical Society, : c2010.,
Description:	xvii, 241 p. :ill. ;26 cm.
Subject:	Functional analysis. -
ISBN:	9780821852545 (pbk.) :

Quantum functional analysis : = non-coordinate approach /
Khelemskii, A. Ia.(Aleksandr IAkovlevich)

Quantum functional analysis :non-coordinate approach /A. Ya. Helemskii. - Providence, R.I. :American Mathematical Society,c2010. - xvii, 241 p. :ill. ;26 cm. - University lecture series ;v. 56. - University lecture series (Providence, R.I.) ;56..

Includes bibliographical references and index.

Three basic definitions and three principal theorems --Machine generated contents note:

This book contains a systematic presentation of quantum functional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications.

ISBN: 9780821852545 (pbk.) :US51.00

LCCN: 2010023811Subjects--Topical Terms:

531838
Functional analysis.

LC Class. No.: QA321 / .K545 2010

Dewey Class. No.: 515/.7

Quantum functional analysis : = non-coordinate approach /
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010 $a 2010023811
020 $a 9780821852545 (pbk.) : $c US51.00
020 $a 082185254X (pbk.)
029 1 $a AU@ $b 000045765077
035 $a (OCoLC)643568735
035 $a AS-BW-100-N-03
040 $a DLC $c DLC $d YDX $d YDXCP $d IAL $d INU $d UKMGB
049 $a FISA
050 0 0 $a QA321 $b .K545 2010
082 0 0 $a 515/.7 $2 22
100 1 $a Khelemskii, A. Ia.(Aleksandr IAkovlevich) $3 1306243
245 1 0 $a Quantum functional analysis : $b non-coordinate approach / $c A. Ya. Helemskii.
260 # $a Providence, R.I. : $b American Mathematical Society, $c c2010.
300 $a xvii, 241 p. : $b ill. ; $c 26 cm.
490 1 $a University lecture series ; $v v. 56
504 $a Includes bibliographical references and index.
505 0 0 $g Machine generated contents note: $g ch. 0 $t Three basic definitions and three principal theorems -- $g ch. 1 $t Preparing the stage -- $g 1.1. $t Operators on normed spaces -- $g 1.2. $t Operators on Hilbert spaces -- $g 1.3. $t The diamond multiplication -- $g 1.4. $t Bimodules -- $g 1.5. $t Amplifications of linear spaces -- $g 1.6. $t Amplifications of linear and bilinear operators -- $g 1.7. $t Spatial tensor products of operator spaces -- $g 1.8. $t Involutive algebras and C*-algebras -- $g 1.9. $t A technical lemma -- $g ch. 2 $t Abstract operator (= quantum) spaces -- $g 2.1. $t Semi-normed bimodules -- $g 2.2. $t Protoquantum and abstract operator (= quantum) spaces. General properties -- $g 2.3. $t First examples. Concrete quantizations -- $g ch. 3 $t Completely bounded operators -- $g 3.1. $t Principal definitions and counterexamples -- $g 3.2. $t Conditions of automatic complete boundedness, and applications -- $g 3.3. $t The repeated quantization -- $g 3.4. $t The complete boundedness and spatial tensor products -- $g ch. 4 $t The completion of abstract operator spaces
505 0 0 $g Ch. 5 $t Strongly and weakly completely bounded bilinear operators -- $g 5.1. $t General definitions and properties -- $g 5.2. $t Examples and counterexamples -- $g ch. 6 $t New preparations: Classical tensor products -- $g 6.1. $t Tensor products of normed spaces -- $g 6.2. $t Tensor products of normed modules -- $g ch. 7 $t Quantum tensor products -- $g 7.0. $t The general universal property -- $g 7.1. $t The Haagerup tensor product -- $g 7.2. $t The operator-projective tensor product -- $g 7.3. $t The operator-injective tensor product -- $g 7.1. $t Column and row Hilbertian spaces as tensor factors -- $g 7.5. $t Functorial properties of quantum tensor products -- $g 7.6. $t Algebraic properties of quantum tensor multiplications -- $g ch. 8 $t Quantum duality -- $g 8.1. $t Quantization of spaces in duality -- $g 8.2. $t Quantum dual and quantum predual space -- $g 8.3. $t Examples -- $g 8.4. $t The self-dual Hilbertian space of Pisier -- $g 8.5. $t Duality and quantum tensor products -- $g 8.6. $t Quantization of spaces, set in vector duality -- $g 8.7. $t Quantization of the space of completely bounded operators -- $g 8.8. $t Quantum adjoint associativity
505 0 0 $g Ch. 9 $t Extreme flatness and the Extension Theorem -- $g 9.0. $t New preparations: More about module tensor products -- $g 9.1. $t One-sided Ruan modules -- $g 9.2. $t Extreme flatness and extreme injectivity -- $g 9.3. $t Extreme flatness of certain modules -- $g 9.4. $t The Arveson[-]Wittstock Theorem -- $g ch. 10 $t Representation Theorem and its gifts -- $g 10.1. $t The Ruan Theorem -- $g 10.2. $t The fulfillment of earlier promises -- $g ch. 11 $t Decomposition Theorem -- $g 11.1. $t Complete positivity and the Stinespring Theorem -- $g 11.2. $t Complete positivity and complete boundedness: An interplay -- $g 11.3. $t Paulsen trick and the Decomposition Theorem -- $g ch. 12 $t Returning to the Haagerup tensor product -- $g 12.1. $t Alternative approach to the Haagerup tensor product -- $g 12.2. $t Decomposition of multilinear operators -- $g 12.3. $t Self-duality of the Haagerup tensor product -- $g ch. 13 $t Miscellany: More examples, facts and applications -- $g 13.1. $t CAR operator space -- $g 13.2. $t Further examples -- $g 13.3. $t Schur and Herz[-]Schur multipliers.
520 # $a This book contains a systematic presentation of quantum functional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications.
520 # $a The approach taken in this book differs significantly from the standard approach used in studying operator space theory. Instead of viewing "quantized coefficients" as matrices in a fixed basis, in this book they are interpreted as finite rank operators in a fixed Hilbert space. This allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject.
520 # $a The book can be used by graduate students and research mathematicians interested in functional analysis and related areas of mathematics and mathematical physics. Prerequisites include standard courses in abstract algebra and functional analysis. --Book Jacket.
650 # 0 $a Functional analysis. $3 531838
650 # 0 $a Operator spaces. $3 629820
830 0 $a University lecture series (Providence, R.I.) ; $v 56. $3 1306041