Linear Operators: General theory |
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Page 251
... orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with D = M then ED = D and , since ( I - D ) CH M , we see that = E ( I – D ) = 0. Thus D = ED + E ( I – D ) ...
... orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with D = M then ED = D and , since ( I - D ) CH M , we see that = E ( I – D ) = 0. Thus D = ED + E ( I – D ) ...
Page 357
... Orthogonal Series and Analytic Functions The following set of exercises is concerned with the application of linear space methods to the theory of orthogonal series . The most important special case of this theory is that of Fourier ...
... Orthogonal Series and Analytic Functions The following set of exercises is concerned with the application of linear space methods to the theory of orthogonal series . The most important special case of this theory is that of Fourier ...
Page 851
... Orthogonal complement of a set in a normed space , II.4.17 ( 72 ) remarks on , ( 93 ) Orthogonal elements and manifolds in Hilbert space , IV.4.3 ( 249 ) Orthogonal projections in Hilbert spaces , IV.4.8 ( 250 ) Orthogonal series ...
... Orthogonal complement of a set in a normed space , II.4.17 ( 72 ) remarks on , ( 93 ) Orthogonal elements and manifolds in Hilbert space , IV.4.3 ( 249 ) Orthogonal projections in Hilbert spaces , IV.4.8 ( 250 ) Orthogonal series ...
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