Linear Operators: General theory |
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... multiplicity . Chelsea , New York , 1951 . 7. Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press , Princeton , 1942 . 8 . An ergodic theorem . Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) ...
... multiplicity . Chelsea , New York , 1951 . 7. Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press , Princeton , 1942 . 8 . An ergodic theorem . Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ