A Hilbert Space Problem Book

Description

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." Front Matter....Pages i-xvii Front Matter....Pages 1-1 Vectors....Pages 3-8 Spaces....Pages 9-11 Weak Topology....Pages 12-16 Analytic Functions....Pages 17-22 Infinite Matrices....Pages 23-26 Boundedness and Invertibility....Pages 27-32 Multiplication Operators....Pages 33-37 Operator Matrices....Pages 38-40 Properties of Spectra....Pages 41-43 Examples of Spectra....Pages 44-46 Spectral Radius....Pages 47-53 Norm Topology....Pages 54-58 Operator Topologies....Pages 59-62 Strong Operator Topology....Pages 63-65 Partial Isometries....Pages 66-73 Polar Decomposition....Pages 74-76 Unilateral Shift....Pages 77-85 Cyclic Vectors....Pages 86-89 Properties of Compactness....Pages 90-97 Examples of Compactness....Pages 98-102 Front Matter....Pages 1-1 Subnormal Operators....Pages 103-111 Numerical Range....Pages 112-119 Unitary Dilations....Pages 120-127 Commutators....Pages 128-134 Toeplitz Operators....Pages 135-140 Front Matter....Pages 141-141 Vectors....Pages 143-143 Spaces....Pages 143-144 Weak Topology....Pages 144-145 Analytic Functions....Pages 145-146 Infinite Matrices....Pages 146-147 Boundedness and Invertibility....Pages 147-147 Multiplication Operators....Pages 148-148 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 151-151 Operator Topologies....Pages 152-152 Strong Operator Topology....Pages 152-153 Partial Isometries....Pages 153-154 Front Matter....Pages 141-141 Polar Decomposition....Pages 154-154 Unilateral Shift....Pages 154-156 Cyclic Vectors....Pages 156-157 Properties of Compactness....Pages 157-158 Examples of Compactness....Pages 158-158 Subnormal Operators....Pages 159-160 Numerical Range....Pages 160-161 Unitary Dilations....Pages 161-162 Commutators....Pages 162-163 Toeplitz Operators....Pages 163-164 Front Matter....Pages 165-165 Vectors....Pages 167-175 Spaces....Pages 176-178 Weak Topology....Pages 179-186 Analytic Functions....Pages 187-198 Infinite Matrices....Pages 199-202 Boundedness and Invertibility....Pages 203-209 Multiplication Operators....Pages 210-216 Operator Matrices....Pages 217-221 Properties of Spectra....Pages 222-225 Examples of Spectra....Pages 226-230 Front Matter....Pages 165-165 Spectral Radius....Pages 231-238 Norm Topology....Pages 239-245 Operator Topologies....Pages 246-250 Strong Operator Topology....Pages 251-255 Partial Isometries....Pages 256-261 Polar Decomposition....Pages 262-266 Unilateral Shift....Pages 267-280 Cyclic Vectors....Pages 281-287 Properties of Compactness....Pages 288-297 Examples of Compactness....Pages 298-303 Subnormal Operators....Pages 304-313 Numerical Range....Pages 314-321 Unitary Dilations....Pages 322-328 Commutators....Pages 329-337 Toeplitz Operators....Pages 338-346 Back Matter....Pages 347-374