Geometry of Linear 2-normed Spaces
Author: Raymond W. Freese
Publisher: Nova Publishers
Published: 2001
Total Pages: 314
ISBN-13: 9781590330197
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Author: Raymond W. Freese
Publisher: Nova Publishers
Published: 2001
Total Pages: 314
ISBN-13: 9781590330197
DOWNLOAD EBOOKAuthor: Robert Gardner Bartle
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 186
ISBN-13: 0821850571
DOWNLOAD EBOOKFeatures 17 papers that resulted from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. This work is suitable for researchers and graduate students in functional analysis.
Author: R. G. Birtle
Publisher:
Published: 1986
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: L. M. Kelly
Publisher: Springer
Published: 2006-11-14
Total Pages: 257
ISBN-13: 3540379460
DOWNLOAD EBOOKAuthor: J. Diestel
Publisher: Lecture Notes in Mathematics
Published: 1975-09
Total Pages: 302
ISBN-13:
DOWNLOAD EBOOKAuthor: Charles Chidume
Publisher: Springer Science & Business Media
Published: 2009-03-27
Total Pages: 337
ISBN-13: 1848821891
DOWNLOAD EBOOKThe contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
Author: Margaret Ann Tevis Herzog
Publisher:
Published: 1959
Total Pages: 62
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher: Elsevier
Published: 2011-10-10
Total Pages: 321
ISBN-13: 0080871798
DOWNLOAD EBOOKIntroduction to Banach Spaces and their Geometry
Author: Jesús Ferrer
Publisher: Springer Nature
Published: 2023-03-14
Total Pages: 140
ISBN-13: 3031236769
DOWNLOAD EBOOKThis brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.
Author: Gilles Godefroy
Publisher: American Mathematical Society
Published: 2024-03-27
Total Pages: 358
ISBN-13: 1470475707
DOWNLOAD EBOOKThis book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.