Linear Operators: General theory |
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Page 145
... uniformly on S - E . The sequence { f } converges μ - uniformly to the function f if for each & > 0 there is a set E e Σ such that v ( μ , E ) < ɛ and such that { f } converges uniformly to f on S - E . It is clear that u - uniform ...
... uniformly on S - E . The sequence { f } converges μ - uniformly to the function f if for each & > 0 there is a set E e Σ such that v ( μ , E ) < ɛ and such that { f } converges uniformly to f on S - E . It is clear that u - uniform ...
Page 314
... uniformly for 22 € VK . It is then clear that u tive element of ba ( S , E ) such that lim λ ( E ) μ ( E ) -0 = H2 ( E ) → 0 V - 1 ( μ2 ) is a non - nega- = 0 uniformly for λ € K . To prove the converse , suppose there exists a non ...
... uniformly for 22 € VK . It is then clear that u tive element of ba ( S , E ) such that lim λ ( E ) μ ( E ) -0 = H2 ( E ) → 0 V - 1 ( μ2 ) is a non - nega- = 0 uniformly for λ € K . To prove the converse , suppose there exists a non ...
Page 360
... uniformly for x in some neighborhood of p . 21 Show that if | ső E „ ( x , z ) dz | ≤M , then the convergence of ... uniformly for every f in AC . Show that there exists a finite constant K such that for f in CBV , | ( Snf ) ( x ) | ≤K ...
... uniformly for x in some neighborhood of p . 21 Show that if | ső E „ ( x , z ) dz | ≤M , then the convergence of ... uniformly for every f in AC . Show that there exists a finite constant K such that for f in CBV , | ( Snf ) ( x ) | ≤K ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ