Linear Operators: General theory |
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Page 1
Neal Jay Plotkin. I. Introduction The spectral theorem is one of the most important theorems of analysis , and possibly is also the theorem with the greatest number of different proofs . The theorem is really a number of different theorems ...
Neal Jay Plotkin. I. Introduction The spectral theorem is one of the most important theorems of analysis , and possibly is also the theorem with the greatest number of different proofs . The theorem is really a number of different theorems ...
Page 104
... theorem Mathew's theorems measurable functions Beurling's theorems Moore's theorems Bochner's theorem canonical basis multiplicity ... theorem von Neumann's theorem Kolmogorov's extension theorem ( see spectral theorem ) Lebesgue spectrum.
... theorem Mathew's theorems measurable functions Beurling's theorems Moore's theorems Bochner's theorem canonical basis multiplicity ... theorem von Neumann's theorem Kolmogorov's extension theorem ( see spectral theorem ) Lebesgue spectrum.
Page 217
Sameer Chavan, Gadadhar Misra. Appendix C The Spectral Theorem This appendix is devoted to the various forms of spectral theorems for normal operators used in this book . We also present several applications of the spectral theorem .
Sameer Chavan, Gadadhar Misra. Appendix C The Spectral Theorem This appendix is devoted to the various forms of spectral theorems for normal operators used in this book . We also present several applications of the spectral theorem .
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ