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
IV
8
V
17
VI
24
VII
35
VIII
41
IX
49
X
59
XXVII
303
XXVIII
317
XXIX
335
XXX
344
XXXII
344
XXXIII
362
XXXIV
380
XXXV
393

XI
107
XII
113
XIII
135
XIV
136
XV
159
XVI
183
XVII
201
XVIII
209
XIX
221
XX
233
XXI
243
XXII
254
XXIII
262
XXIV
268
XXV
281
XXVI
293
XXXVI
403
XXXVII
417
XXXVIII
418
XXXIX
433
XL
451
XLI
471
XLII
485
XLIII
496
XLIV
509
XLV
513
XLVI
519
XLVII
531
XLIX
537
L
555
LI
559
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