An Introduction to Banach Space Theory

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Springer Science & Business Media, Oct 9, 1998 - Mathematics - 596 pages
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Many important reference works in Banach space theory have appeared since Banach's "Théorie des Opérations Linéaires", the impetus for the development of much of the modern theory in this field. While these works are classical starting points for the graduate student wishing to do research in Banach space theory, they can be formidable reading for the student who has just completed a course in measure theory and integration that introduces the L_p spaces and would like to know more about Banach spaces in general. The purpose of this book is to bridge this gap and provide an introduction to the basic theory of Banach spaces and functional analysis. It prepares students for further study of both the classical works and current research. It is accessible to students who understand the basic properties of L_p spaces but have not had a course in functional analysis. The book is sprinkled liberally with examples, historical notes, and references to original sources. Over 450 exercises provide supplementary examples and counterexamples and give students practice in the use of the results developed in the text.
 

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Contents

II
1
III
8
IV
17
V
24
VI
35
VII
41
VIII
49
IX
59
XXVI
305
XXVII
319
XXVIII
339
XXIX
349
XXX
350
XXXI
368
XXXII
386
XXXIII
399

X
109
XI
115
XII
137
XIII
138
XIV
161
XV
185
XVI
203
XVII
211
XVIII
223
XIX
235
XX
245
XXI
256
XXII
264
XXIII
270
XXIV
283
XXV
295
XXXIV
411
XXXV
425
XXXVI
426
XXXVII
441
XXXVIII
459
XXXIX
479
XL
493
XLI
504
XLII
517
XLIII
521
XLIV
529
XLV
541
XLVI
547
XLVII
565
XLVIII
569
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Funktionalanalysis
Dirk Werner
No preview available - 2007
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About the author (1998)

Megginson-University of Michigan, Ann Arbor

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