INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783034804783
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52286
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Functional Analysis in Asymmetric Normed Space
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by ??tefan Cobza??
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Basel
Name of Publisher, Distributor, etc.
: Springer Basel :Imprint: Birkh?nuser,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
X, 219 p. 1 illus. in color., online resource.
SERIES
Series Title
(Frontiers in Mathematics,1660-8046)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn-Banach type theorems and separation results for convex sets, Krein-Milman type theorems, analogs of the fundamental principles - open mapping, closed graph and uniform boundedness theorems - an analog of the Schauder's theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis - completeness, compactness and Baire category - which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject.Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text.
Text of Note
Introduction.-1. Quasi-metric and Quasi-uniform Spaces. 1.1. Topological properties of quasi-metric and quasi-uniform spaces -- 1.2. Completeness and compactness in quasi-metric and quasi-uniform spaces.-2. Asymmetric Functional Analysis -- 2.1. Continuous linear operators between asymmetric normed spaces -- 2.2. Hahn-Banach type theorems and the separation of convex sets -- 2.3. The fundamental principles -- 2.4. Weak topologies -- 2.5. Applications to best approximation -- 2.6. Spaces of semi-Lipschitz functions -- Bibliography -- Index.?╗╣
SERIES
Title
Frontiers in Mathematics,1660-8046
TOPICAL NAME USED AS SUBJECT
Mathematics
Functional analysis
Operator theory
Topology
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Cobza??, ??tefan.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783034804776.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783034804776.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
