東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

An invitation to unbounded represent...

Schmudgen, Konrad.

Linked to FindBook

Google Book

Amazon

博客來

An invitation to unbounded representations of ∗-algebras on Hilbert space

Record Type:	Electronic resources : Monograph/item
Title/Author:	An invitation to unbounded representations of ∗-algebras on Hilbert space/ by Konrad Schmudgen.
Author:	Schmudgen, Konrad.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xviii, 381 p. :ill., digital ;24 cm.
[NT 15003449]:	General Notation -- 1 Prologue: The Algebraic Approach to Quantum Theories -- 2 ∗-Algebras -- 3 O-Algebras -- 4 ∗-Representations -- 5 Positive Linear Functionals -- 6 Representations of Tensor Algebras -- 7 Integrable Representations of Commutative ∗-Algebras -- 8 The Weyl Algebra and the Canonical Commutation Relation -- 9 Integrable Representations of Enveloping Algebras -- 10 Archimedean Quadratic Modules and Positivstellensatze -- 11 The Operator Relation XX=F(XX) -- 12 Induced ∗-Representations -- 13 Well-behaved ∗-Representations -- 14 Representations on Rigged Spaces and Hilbert C-modules. A Unbounded Operators on Hilbert Space -- B C*-Algebras and Representations -- C Locally Convex Spaces and Separation of Convex Sets -- References -- Symbol Index -- Subject Index.
Contained By:	Springer Nature eBook
Subject:	Hilbert space. -
Online resource:	https://doi.org/10.1007/978-3-030-46366-3
ISBN:	9783030463663

An invitation to unbounded representations of ∗-algebras on Hilbert space
Schmudgen, Konrad.

An invitation to unbounded representations of ∗-algebras on Hilbert space[electronic resource] /by Konrad Schmudgen. - Cham :Springer International Publishing :2020. - xviii, 381 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2850072-5285 ;. - Graduate texts in mathematics ;285..

General Notation -- 1 Prologue: The Algebraic Approach to Quantum Theories -- 2 ∗-Algebras -- 3 O*-Algebras -- 4 ∗-Representations -- 5 Positive Linear Functionals -- 6 Representations of Tensor Algebras -- 7 Integrable Representations of Commutative ∗-Algebras -- 8 The Weyl Algebra and the Canonical Commutation Relation -- 9 Integrable Representations of Enveloping Algebras -- 10 Archimedean Quadratic Modules and Positivstellensatze -- 11 The Operator Relation XX*=F(X*X) -- 12 Induced ∗-Representations -- 13 Well-behaved ∗-Representations -- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space -- B C*-Algebras and Representations -- C Locally Convex Spaces and Separation of Convex Sets -- References -- Symbol Index -- Subject Index.

This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensatze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

ISBN: 9783030463663

Standard No.: 10.1007/978-3-030-46366-3doiSubjects--Topical Terms:

558371
Hilbert space.

LC Class. No.: QA322.4

Dewey Class. No.: 515.733

An invitation to unbounded representations of ∗-algebras on Hilbert space
LDR:03093nmm a2200337 a 4500 001 2222677
003 DE-He213
005 20201123115906.0
006 m d
007 cr nn 008maaau
008 210108s2020 sz s 0 eng d
020 $a 9783030463663 $q (electronic bk.)
020 $a 9783030463656 $q (paper)
024 7 $a 10.1007/978-3-030-46366-3 $2 doi
035 $a 978-3-030-46366-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA322.4
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.733 $2 23
090 $a QA322.4 $b .S356 2020
100 1 $a Schmudgen, Konrad. $3 3270360
245 1 3 $a An invitation to unbounded representations of ∗-algebras on Hilbert space $h [electronic resource] / $c by Konrad Schmudgen.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xviii, 381 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 285
505 0 $a General Notation -- 1 Prologue: The Algebraic Approach to Quantum Theories -- 2 ∗-Algebras -- 3 O*-Algebras -- 4 ∗-Representations -- 5 Positive Linear Functionals -- 6 Representations of Tensor Algebras -- 7 Integrable Representations of Commutative ∗-Algebras -- 8 The Weyl Algebra and the Canonical Commutation Relation -- 9 Integrable Representations of Enveloping Algebras -- 10 Archimedean Quadratic Modules and Positivstellensatze -- 11 The Operator Relation XX*=F(X*X) -- 12 Induced ∗-Representations -- 13 Well-behaved ∗-Representations -- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space -- B C*-Algebras and Representations -- C Locally Convex Spaces and Separation of Convex Sets -- References -- Symbol Index -- Subject Index.
520 $a This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensatze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
650 0 $a Hilbert space. $3 558371
650 0 $a Hilbert algebras. $3 888650
650 0 $a Operator algebras. $3 579171
650 1 4 $a Operator Theory. $3 897311
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Topological Groups, Lie Groups. $3 891005
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 285. $3 3461642
856 4 0 $u https://doi.org/10.1007/978-3-030-46366-3
950 $a Mathematics and Statistics (SpringerNature-11649)