Introduction to Tensor Products of Banach Spaces

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Springer Science & Business Media, Jan 15, 2002 - Mathematics - 226 pages
This book is intended as an introduction to the theory of tensor products of Banach spaces. The prerequisites for reading the book are a first course in Functional Analysis and in Measure Theory, as far as the Radon-Nikodym theorem. The book is entirely self-contained and two appendices give addi tional material on Banach Spaces and Measure Theory that may be unfamil iar to the beginner. No knowledge of tensor products is assumed. Our viewpoint is that tensor products are a natural and productive way to understand many of the themes of modern Banach space theory and that "tensorial thinking" yields insights into many otherwise mysterious phenom ena. We hope to convince the reader of the validity of this belief. We begin in Chapter 1 with a treatment of the purely algebraic theory of tensor products of vector spaces. We emphasize the use of the tensor product as a linearizing tool and we explain the use of tensor products in the duality theory of spaces of operators in finite dimensions. The ideas developed here, though simple, are fundamental for the rest of the book.
 

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Contents

I
1
III
5
IV
7
V
9
VI
10
VII
12
VIII
15
X
22
XXX
103
XXXI
108
XXXII
114
XXXIII
122
XXXIV
125
XXXV
127
XXXVII
133
XXXVIII
140

XI
25
XII
30
XIII
32
XIV
39
XV
42
XVI
45
XVIII
49
XIX
51
XX
57
XXI
62
XXII
68
XXIII
71
XXV
82
XXVI
87
XXVII
91
XXVIII
93
XXXIX
152
XL
157
XLI
159
XLIII
165
XLIV
170
XLV
176
XLVI
184
XLVII
187
XLIX
194
L
198
LI
201
LII
205
LIII
211
LIV
219
LV
223
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