Yau-Chuen Wong

Introductory Theory of Topological Vector SPates (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 440
• Erscheinungstermin: 25. Januar 2019
• Englisch
• ISBN-13: 9781351436458
• Artikelnr.: 54957741

Autorenporträt

Wong\, Yau-Chuen

Inhaltsangabe

Hahn-Banach's Extension Theorem
Banach spaces and Hilbert spaces
operators and some consequences of Hahn-Banach's Extension Theorem
the Uniform Boundedness Theorem and Banach's Open Mapping Theorem
a structure theorem for compact sets in a Banach space
topological injections and topological surjections
vector topologies
separation theorems and Krein-Milman's Theorem
projective topologies and inductive topologies
normed spaces associated with a locally convex space
vector bornologies
initial bornologies and final bornologies
von Neumann bornologies and locally convex topologies determined by convex bornologies
dual pairs and the weak topologies
elementary duality theory
semi-reflexive spaces and ultra-semi-reflexive spaces
some recent results on compact operators and weakly compact operators
precompact seminorms and Schwartz spaces
elementary Riesz - Schauder's theory
an introduction to operator ideals
an aspect of fixed point theory
an inrtoduction to ordered convex spaces.