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001 ocn643568735;

003 OCoLC;

005 20141212100934.0;

008 100622s2010 riua b 001 0 eng ;

010 a| 2010023811;

016 7 a| 0157605652| Uk;

020 a| 9780821852545 (pbk. : alk. paper);

020 a| 082185254X (pbk. : alk. paper);

029 1 a| AU@b| 000045765077;

029 1 a| DEBBGb| BV026936321;

029 1 a| NZ1b| 13939935;

035 a| (Sirsi) a2810752;

035 a| (OCoLC)643568735;

035 a| 99947865793;

049 a| EREE;

050 00 a| QA321b| .K545 2010;

082 00 a| 515/.72| 22;

100 1 a| Khelemskiĭ, A. I͡A︡.q| (Aleksandr I͡A︡kovlevich)=| ^A327035;

245 10 a| Quantum functional analysis :b| non-coordinate approach /c| A. Ya. Helemskii.;

300 a| xvii, 241 pages :b| illustrations ;c| 26 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| University lecture series ;v| v. 56;

504 a| Includes bibliographical references and index.;

505 00 g| Machine generated contents note:g| ch. 0t| Three basic definitions and three principal theorems --g| ch. 1t| 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. 2t| 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. 3t| 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. 4t| The completion of abstract operator spaces;

505 00 g| Ch. 5t| Strongly and weakly completely bounded bilinear operators --g| 5.1.t| General definitions and properties --g| 5.2.t| Examples and counterexamples --g| ch. 6t| 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. 7t| 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. 8t| 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 00 g| Ch. 9t| 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. 10t| Representation Theorem and its gifts --g| 10.1.t| The Ruan Theorem --g| 10.2.t| The fulfillment of earlier promises --g| ch. 11t| 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. 12t| 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. 13t| 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.=| ^A16456;

650 0 a| Operator spaces.=| ^A561143;

650 07 a| Funktionalanalysis.0| (DE-588c)4018916-8.2| swd;

650 07 a| Operatorraum.0| (DE-588c)4591231-2.2| swd;

830 0 a| University lecture series (Providence, R.I.) ;v| 56.=| ^A344893;

856 4 u| http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=4087611&custom_att_2=simple_viewery| Quantum functional analysisx| Inhaltsverzeichnis;

938 a| YBP Library Servicesb| YANKn| 3413237;

949 a| QA321 .K545 2010h| Joyner48i| 30372013855710o| jjlm;

910 a| PromptCat;

994 a| 92b| ERE;

596 a| 1;

998 a| 2810752;

999 a| QA321 .K545 2010w| LCc| 1i| 30372013855710d| 4/5/2013e| 5/21/2012f| 4/5/2013g| 2l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 5/16/2012x| BOOKz| JSTACKSo| .STAFF. jjlm;

Quantum functional analysis : non-coordinate approach / A. Ya. Helemskii.

Author/creator	Khelemskiĭ, A. I͡A︡
Format	Book
Publication Info	Providence, R.I. : American Mathematical Society, ©2010.
Description	xvii, 241 pages : illustrations ; 26 cm.
Supplemental Content	Quantum functional analysis
Subjects	Functional analysis. Operator spaces.

Series	University lecture series ; v. 56 University lecture series (Providence, R.I.) ; 56. ^A344893
Contents	Machine generated contents note: ch. 0 Three basic definitions and three principal theorems -- ch. 1 Preparing the stage -- 1.1. Operators on normed spaces -- 1.2. Operators on Hilbert spaces -- 1.3. The diamond multiplication -- 1.4. Bimodules -- 1.5. Amplifications of linear spaces -- 1.6. Amplifications of linear and bilinear operators -- 1.7. Spatial tensor products of operator spaces -- 1.8. Involutive algebras and C*-algebras -- 1.9. A technical lemma -- ch. 2 Abstract operator (= quantum) spaces -- 2.1. Semi-normed bimodules -- 2.2. Protoquantum and abstract operator (= quantum) spaces. General properties -- 2.3. First examples. Concrete quantizations -- ch. 3 Completely bounded operators -- 3.1. Principal definitions and counterexamples -- 3.2. Conditions of automatic complete boundedness, and applications -- 3.3. The repeated quantization -- 3.4. The complete boundedness and spatial tensor products -- ch. 4 The completion of abstract operator spaces
Contents	Ch. 5 Strongly and weakly completely bounded bilinear operators -- 5.1. General definitions and properties -- 5.2. Examples and counterexamples -- ch. 6 New preparations: Classical tensor products -- 6.1. Tensor products of normed spaces -- 6.2. Tensor products of normed modules -- ch. 7 Quantum tensor products -- 7.0. The general universal property -- 7.1. The Haagerup tensor product -- 7.2. The operator-projective tensor product -- 7.3. The operator-injective tensor product -- 7.1. Column and row Hilbertian spaces as tensor factors -- 7.5. Functorial properties of quantum tensor products -- 7.6. Algebraic properties of quantum tensor multiplications -- ch. 8 Quantum duality -- 8.1. Quantization of spaces in duality -- 8.2. Quantum dual and quantum predual space -- 8.3. Examples -- 8.4. The self-dual Hilbertian space of Pisier -- 8.5. Duality and quantum tensor products -- 8.6. Quantization of spaces, set in vector duality -- 8.7. Quantization of the space of completely bounded operators -- 8.8. Quantum adjoint associativity
Contents	Ch. 9 Extreme flatness and the Extension Theorem -- 9.0. New preparations: More about module tensor products -- 9.1. One-sided Ruan modules -- 9.2. Extreme flatness and extreme injectivity -- 9.3. Extreme flatness of certain modules -- 9.4. The Arveson[-]Wittstock Theorem -- ch. 10 Representation Theorem and its gifts -- 10.1. The Ruan Theorem -- 10.2. The fulfillment of earlier promises -- ch. 11 Decomposition Theorem -- 11.1. Complete positivity and the Stinespring Theorem -- 11.2. Complete positivity and complete boundedness: An interplay -- 11.3. Paulsen trick and the Decomposition Theorem -- ch. 12 Returning to the Haagerup tensor product -- 12.1. Alternative approach to the Haagerup tensor product -- 12.2. Decomposition of multilinear operators -- 12.3. Self-duality of the Haagerup tensor product -- ch. 13 Miscellany: More examples, facts and applications -- 13.1. CAR operator space -- 13.2. Further examples -- 13.3. Schur and Herz[-]Schur multipliers.
Abstract	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.
Abstract	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.
Abstract	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.
Bibliography note	Includes bibliographical references and index.
LCCN	2010023811
ISBN	9780821852545 (pbk. : alk. paper)
ISBN	082185254X (pbk. : alk. paper)

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Quantum functional analysis : non-coordinate approach / A. Ya. Helemskii.

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