語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Bilinear maps and tensor products in...
~
Kubrusly, Carlos S.
FindBook
Google Book
Amazon
博客來
Bilinear maps and tensor products in operator theory
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Bilinear maps and tensor products in operator theory/ by Carlos S. Kubrusly.
作者:
Kubrusly, Carlos S.
出版者:
Cham :Springer International Publishing : : 2023.,
面頁冊數:
xiv, 254 p. :illustrations, digital ;24 cm.
內容註:
Preface -- 1. Linear-Space Results -- 2. Bilinear Maps: Algebraic Aspects -- 3. Algebraic Tensor Product -- 4. Interpretations -- 5. Normed-Space Results -- 6. Bounded Bilinear Maps -- 7. Norms on Tensor Products -- 8. Operator Norms -- 9. Tensor Product Operators -- References -- List of Symbols -- Index.
Contained By:
Springer Nature eBook
標題:
Operator theory. -
電子資源:
https://doi.org/10.1007/978-3-031-34093-2
ISBN:
9783031340932
Bilinear maps and tensor products in operator theory
Kubrusly, Carlos S.
Bilinear maps and tensor products in operator theory
[electronic resource] /by Carlos S. Kubrusly. - Cham :Springer International Publishing :2023. - xiv, 254 p. :illustrations, digital ;24 cm. - Universitext,2191-6675. - Universitext..
Preface -- 1. Linear-Space Results -- 2. Bilinear Maps: Algebraic Aspects -- 3. Algebraic Tensor Product -- 4. Interpretations -- 5. Normed-Space Results -- 6. Bounded Bilinear Maps -- 7. Norms on Tensor Products -- 8. Operator Norms -- 9. Tensor Product Operators -- References -- List of Symbols -- Index.
This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. Tensor products, particularly in infinite-dimensional normed spaces, are heavily based on bilinear maps. The author brings these topics together by using bilinear maps as an auxiliary, yet fundamental, tool for accomplishing a consistent, useful, and straightforward theory of tensor products. The author's usual clear, friendly, and meticulously prepared exposition presents the material in ways that are designed to make grasping concepts easier and simpler. The approach to the subject is uniquely presented from an operator theoretic view. An introductory course in functional analysis is assumed. In order to keep the prerequisites as modest as possible, there are two introductory chapters, one on linear spaces (Chapter 1) and another on normed spaces (Chapter 5), summarizing the background material required for a thorough understanding. The reader who has worked through this text will be well prepared to approach more advanced texts and additional literature on the subject. The book brings the theory of tensor products on Banach spaces to the edges of Grothendieck's theory, and changes the target towards tensor products of bounded linear operators. Both Hilbert-space and Banach-space operator theory are considered and compared from the point of view of tensor products. This is done from the first principles of functional analysis up to current research topics, with complete and detailed proofs. The first four chapters deal with the algebraic theory of linear spaces, providing various representations of the algebraic tensor product defined in an axiomatic way. Chapters 5 and 6 give the necessary background concerning normed spaces and bounded bilinear mappings. Chapter 7 is devoted to the study of reasonable crossnorms on tensor product spaces, discussing in detail the important extreme realizations of injective and projective tensor products. In Chapter 8 uniform crossnorms are introduced in which the tensor products of operators are bounded; special attention is paid to the finitely generated situation. The concluding Chapter 9 is devoted to the study of the Hilbert space setting and the spectral properties of the tensor products of operators. Each chapter ends with a section containing "Additional Propositions" and suggested readings for further studies.
ISBN: 9783031340932
Standard No.: 10.1007/978-3-031-34093-2doiSubjects--Topical Terms:
542531
Operator theory.
LC Class. No.: QA329 / .K83 2023
Dewey Class. No.: 515.724
Bilinear maps and tensor products in operator theory
LDR
:03829nmm a2200337 a 4500
001
2336252
003
DE-He213
005
20231114013954.0
006
m d
007
cr nn 008maaau
008
240402s2023 sz s 0 eng d
020
$a
9783031340932
$q
(electronic bk.)
020
$a
9783031340925
$q
(paper)
024
7
$a
10.1007/978-3-031-34093-2
$2
doi
035
$a
978-3-031-34093-2
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA329
$b
.K83 2023
072
7
$a
PBKF
$2
bicssc
072
7
$a
MAT037000
$2
bisacsh
072
7
$a
PBKF
$2
thema
082
0 4
$a
515.724
$2
23
090
$a
QA329
$b
.K95 2023
100
1
$a
Kubrusly, Carlos S.
$3
2162994
245
1 0
$a
Bilinear maps and tensor products in operator theory
$h
[electronic resource] /
$c
by Carlos S. Kubrusly.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2023.
300
$a
xiv, 254 p. :
$b
illustrations, digital ;
$c
24 cm.
490
1
$a
Universitext,
$x
2191-6675
505
0
$a
Preface -- 1. Linear-Space Results -- 2. Bilinear Maps: Algebraic Aspects -- 3. Algebraic Tensor Product -- 4. Interpretations -- 5. Normed-Space Results -- 6. Bounded Bilinear Maps -- 7. Norms on Tensor Products -- 8. Operator Norms -- 9. Tensor Product Operators -- References -- List of Symbols -- Index.
520
$a
This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. Tensor products, particularly in infinite-dimensional normed spaces, are heavily based on bilinear maps. The author brings these topics together by using bilinear maps as an auxiliary, yet fundamental, tool for accomplishing a consistent, useful, and straightforward theory of tensor products. The author's usual clear, friendly, and meticulously prepared exposition presents the material in ways that are designed to make grasping concepts easier and simpler. The approach to the subject is uniquely presented from an operator theoretic view. An introductory course in functional analysis is assumed. In order to keep the prerequisites as modest as possible, there are two introductory chapters, one on linear spaces (Chapter 1) and another on normed spaces (Chapter 5), summarizing the background material required for a thorough understanding. The reader who has worked through this text will be well prepared to approach more advanced texts and additional literature on the subject. The book brings the theory of tensor products on Banach spaces to the edges of Grothendieck's theory, and changes the target towards tensor products of bounded linear operators. Both Hilbert-space and Banach-space operator theory are considered and compared from the point of view of tensor products. This is done from the first principles of functional analysis up to current research topics, with complete and detailed proofs. The first four chapters deal with the algebraic theory of linear spaces, providing various representations of the algebraic tensor product defined in an axiomatic way. Chapters 5 and 6 give the necessary background concerning normed spaces and bounded bilinear mappings. Chapter 7 is devoted to the study of reasonable crossnorms on tensor product spaces, discussing in detail the important extreme realizations of injective and projective tensor products. In Chapter 8 uniform crossnorms are introduced in which the tensor products of operators are bounded; special attention is paid to the finitely generated situation. The concluding Chapter 9 is devoted to the study of the Hilbert space setting and the spectral properties of the tensor products of operators. Each chapter ends with a section containing "Additional Propositions" and suggested readings for further studies.
650
0
$a
Operator theory.
$3
542531
650
0
$a
Tensor products.
$3
711438
650
0
$a
Algebras, Linear.
$3
521915
650
1 4
$a
Functional Analysis.
$3
893943
650
2 4
$a
Operator Theory.
$3
897311
710
2
$a
SpringerLink (Online service)
$3
836513
773
0
$t
Springer Nature eBook
830
0
$a
Universitext.
$3
812115
856
4 0
$u
https://doi.org/10.1007/978-3-031-34093-2
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
館藏地:
全部
電子資源
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W9462457
電子資源
11.線上閱覽_V
電子書
EB QA329 .K83 2023
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入