Introduction to Functional Analysis

Frontcover
Oxford University Press, 31.07.1997 - 448 Seiten
0 Rezensionen
The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fr--eacute--;chet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fr--eacute--;chet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.
  

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Inhalt

II
3
III
8
IV
13
V
19
VI
29
VII
31
VIII
44
IX
52
XXII
211
XXIII
219
XXIV
236
XXV
247
XXVI
249
XXVII
261
XXVIII
276
XXIX
294

X
59
XI
67
XII
72
XIII
81
XIV
91
XV
101
XVI
117
XVII
137
XVIII
139
XIX
148
XX
179
XXI
197
XXX
306
XXXI
326
XXXII
344
XXXIII
357
XXXIV
378
XXXV
391
XXXVI
404
XXXVII
423
XXXVIII
425
XXXIX
429
XL
433
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