A Hilbert Space Problem Book

P. R. Halmos (auth.)9780387906850, 9783540906858, 0387906851, 3540906851

From the Preface: “This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks… The second part, a very short one, consists of hints… The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem….

This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book.”

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Table of contents :
Front Matter….Pages i-xvii
Front Matter….Pages 1-1
Vectors and spaces….Pages 3-9
Weak topology….Pages 10-14
Analytic functions….Pages 15-20
Infinite matrices….Pages 21-23
Boundedness and invertibility….Pages 24-28
Multiplication operators….Pages 29-33
Operator matrices….Pages 34-36
Properties of spectra….Pages 37-39
Examples of spectra….Pages 40-43
Spectral radius….Pages 44-51
Norm topology….Pages 52-54
Strong and weak topologies….Pages 55-59
Partial isometries….Pages 60-70
Unilateral shift….Pages 71-83
Compact operators….Pages 84-97
Subnormal operators….Pages 98-107
Numerical range….Pages 108-117
Unitary dilations….Pages 118-125
Commutators of operators….Pages 126-134
Toeplitz operators….Pages 135-140
Front Matter….Pages 141-141
Vectors and spaces….Pages 143-143
Weak topology….Pages 144-145
Analytic functions….Pages 145-146
Infinite matrices….Pages 146-146
Boundedness and invertibility….Pages 146-147
Multiplication operators….Pages 147-148
Operator matrices….Pages 148-149
Properties of spectra….Pages 149-149
Examples of spectra….Pages 149-150
Spectral radius….Pages 150-151
Norm topology….Pages 151-152
Strong and weak topologies….Pages 152-152
Partial isometries….Pages 152-154
Unilateral shift….Pages 154-156
Compact operators….Pages 156-158
Subnormal operators….Pages 158-160
Numerical range….Pages 160-161
Unitary dilations….Pages 161-162
Commutators of operators….Pages 162-163
Toeplitz operators….Pages 163-164
Front Matter….Pages 165-165
Vectors and spaces….Pages 167-177
Weak topology….Pages 178-186
Analytic functions….Pages 187-200
Infinite matrices….Pages 201-203
Boundedness and invertibility….Pages 204-208
Multiplication operators….Pages 209-217
Operator matrices….Pages 218-224
Properties of spectra….Pages 225-228
Examples of spectra….Pages 229-235
Spectral radius….Pages 236-244
Norm topology….Pages 245-249
Strong and weak topologies….Pages 250-258
Partial isometries….Pages 259-267
Unilateral shift….Pages 268-285
Compact operators….Pages 286-305
Subnormal operators….Pages 306-316
Numerical Range….Pages 317-325
Unitary dilations….Pages 326-332
Commutators of operators….Pages 333-344
Toeplitz operators….Pages 345-351
Back Matter….Pages 352-365