Functional Analysis

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Krishna Prakashan Media, 1980 - 429 من الصفحات
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المحتويات

Elements of Set Theory 183
1
Basic operations on sets
6
Relations
12
Functions
20
Order
29
Some Properties of real numbers
34
The axiom of choice and its equivalents
35
Cardinality and denumerability
43
Linear transformations or Homomorphism of linear spaces
182
Properties of linear transformations
183
IS Some particular linear transformations
184
Rank and nullity of a linear transformation
186
Linear transformations as vectors
187
Product of linear transformations
189
Algebra or linear algebra
192
Polynomials
193

Decimal Ternary and binary representations
53
CardinalArithmetic
54
Cantors ternary set
70
Order types and ordinal numbers
73
Metric Spaces 84138
84
Euclidean spaces
89
Some important inequalities
92
Solved Examples
93
Bounded and unbounded Metric spaces
101
Spheres or balls
102
Open Sets
105
Closed Sets
108
Neighbourhoods
111
Adherent points
112
Closure interior exterior and boundary of a set
114
Subspaces
117
Dense and nondense sets separable spaces
119
Sequences and subsequences in a metric space
121
Cauchy sequences
123
Complete metric spaces
124
Completeness and contracting mappings
128
Some complete metric spaces
129
Completion of a metric space
136
Linear Spaces 139209
139
General properties of linear spaces
146
Linear subspaces
147
Algebra of subspaces
149
Linear combination of vectors Linear span of a set
150
Linear sum of two subspaces
151
Direct sum of spaces
152
Quotient space
155
Linear dependence and linea independence of vectors
163
Hamel Basis of linear space
166
Dimension of a linear space
170
Isomorphism of linear spaces
172
Invertible or nonsingular linear transformations
194
Linear functionals
197
Linear functionals in finitedimensional spaces
198
Extension theorems for linear transformations
200
Reflexivity
203
Projections
206
CHAPTER 4
210
The classical Banach space Lp
235
Subspaces and Quotient spaces of Banach spaces
241
Continuous linear transformations
249
Equivalent norms
263
Ricszlemma
269
Convexity
270
Linear functionals and the Hahn Banach theorem
273
The natural imbedding of N into A Reflexivity
287
The open mapping theorem
295
Projections on Banach spaces
300
The Closed graph theorem
301
Uniform bounded principle
305
The conjugate of an operator
307
Hilbert Spaces 316398
316
Hilbert spaces
317
Some properties of Hilbert
318
Orthogonal complements
330
Orthonormal sets
336
The Conjugate space H
353
The Adjoint of an operator
361
Self adjoint operators
367
Normal and Unitary operators
373
Perpendicular Projections
384
CHAPTER 6
399
Matrix of a Linear transformation
401
The spectral thumcm
415
Index ivi
431
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