國立虎尾科技大學 |

Topics in Banach Space Theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Topics in Banach Space Theory/ by Fernando Albiac, Nigel J. Kalton.
作者:	Albiac, Fernando.
其他作者:	Kalton, Nigel J.
面頁冊數:	XX, 508 p. 23 illus., 14 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Functional analysis. -
電子資源:	https://doi.org/10.1007/978-3-319-31557-7
ISBN:	9783319315577

Topics in Banach Space Theory
Albiac, Fernando.

Topics in Banach Space Theory[electronic resource] /by Fernando Albiac, Nigel J. Kalton. - 2nd ed. 2016. - XX, 508 p. 23 illus., 14 illus. in color.online resource. - Graduate Texts in Mathematics,233 0072-5285 ;. - Graduate Texts in Mathematics,222.

1. Bases and Basic Sequences -- 2. The Classical Sequence Spaces -- 3. Special Types of Bases -- 4. Banach Spaces of Continuous Functions -- 5. L_{1}(\mu )-Spaces and \mathcal C(K)-Spaces -- 6. The Spaces L_{p} for 1\le p^I Basic probability in use -- Appendix J Generalities on Ultraproducts -- Appendix K The Bochner Integral abridged -- List of Symbols -- References -- Index.

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book…succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly… It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments… I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book…" —Gilles Godefroy, Mathematical Reviews.

ISBN: 9783319315577

Standard No.: 10.1007/978-3-319-31557-7doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Topics in Banach Space Theory
LDR:03574nam a22004095i 4500 001 979618
003 DE-He213
005 20200703235341.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319315577 $9 978-3-319-31557-7
024 7 $a 10.1007/978-3-319-31557-7 $2 doi
035 $a 978-3-319-31557-7
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Albiac, Fernando. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1111743
245 1 0 $a Topics in Banach Space Theory $h [electronic resource] / $c by Fernando Albiac, Nigel J. Kalton.
250 $a 2nd ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XX, 508 p. 23 illus., 14 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 233
505 0 $a 1. Bases and Basic Sequences -- 2. The Classical Sequence Spaces -- 3. Special Types of Bases -- 4. Banach Spaces of Continuous Functions -- 5. L_{1}(\mu )-Spaces and \mathcal C(K)-Spaces -- 6. The Spaces L_{p} for 1\le p^I Basic probability in use -- Appendix J Generalities on Ultraproducts -- Appendix K The Bochner Integral abridged -- List of Symbols -- References -- Index.
520 $a This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book…succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly… It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments… I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book…" —Gilles Godefroy, Mathematical Reviews.
650 0 $a Functional analysis. $3 527706
650 1 4 $a Functional Analysis. $3 672166
700 1 $a Kalton, Nigel J. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1111744
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319315553
776 0 8 $i Printed edition: $z 9783319315560
776 0 8 $i Printed edition: $z 9783319810638
830 0 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222 $3 1254915
856 4 0 $u https://doi.org/10.1007/978-3-319-31557-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)