Linear Operators: General theory |
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Page 253
... correspond- ing equivalence classes and that u € U. Consider an arbitrary ele- ment υβ in the basis { v } for which ( u , v ) 0. It will be shown that Uge V. Since U and V are corresponding classes there are elements 1 υβ - u , Ug in U ...
... correspond- ing equivalence classes and that u € U. Consider an arbitrary ele- ment υβ in the basis { v } for which ( u , v ) 0. It will be shown that Uge V. Since U and V are corresponding classes there are elements 1 υβ - u , Ug in U ...
Page 254
... corresponding equivalence classes U and V determine the same closed linear manifold M. Hence , if one of U and V is finite , M is finite dimensional , and therefore the other of U and V is finite and has the same cardinality . If ...
... corresponding equivalence classes U and V determine the same closed linear manifold M. Hence , if one of U and V is finite , M is finite dimensional , and therefore the other of U and V is finite and has the same cardinality . If ...
Page 720
... corresponding results for a strongly measurable n- parameter semi - group of operators . 16 Show that the convergence almost everywhere in Theorem 6.9 remains valid if ( S , 2 , μ ) is a finite measure space and Ss f ( s ) ( 1 + log + ...
... corresponding results for a strongly measurable n- parameter semi - group of operators . 16 Show that the convergence almost everywhere in Theorem 6.9 remains valid if ( S , 2 , μ ) is a finite measure space and Ss f ( s ) ( 1 + log + ...
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