Linear Operators: General theory |
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Page 294
... weakly sequentially compact , a subsequence of { f } con- verges weakly , and it may be assumed without loss of generality that { f } itself converges weakly . By Theorem 7 , { SEfn ( s ) u ( ds ) } converges for each ΕΕΣ . Let în ( E ) ...
... weakly sequentially compact , a subsequence of { f } con- verges weakly , and it may be assumed without loss of generality that { f } itself converges weakly . By Theorem 7 , { SEfn ( s ) u ( ds ) } converges for each ΕΕΣ . Let în ( E ) ...
Page 314
... weakly sequentially com- pact if and only if there exists a non - negative u in ba ( S , E ) such that 12 uniformly for λε Κ . lim λ ( E ) = 0 μ ( E ) -0 PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let VUT be the ...
... weakly sequentially com- pact if and only if there exists a non - negative u in ba ( S , E ) such that 12 uniformly for λε Κ . lim λ ( E ) = 0 μ ( E ) -0 PROOF . Let KC ba ( S , E ) be weakly sequentially compact and let VUT be the ...
Page 345
... weakly sequentially compact if and only if it is bounded and the set { f ( ) } , ƒ e A , is quasi - equicontinuous . 37 Let D be a bounded domain . Show that a sequence of func- tions in A ( D ) is a weak Cauchy sequence ( a sequence ...
... weakly sequentially compact if and only if it is bounded and the set { f ( ) } , ƒ e A , is quasi - equicontinuous . 37 Let D be a bounded domain . Show that a sequence of func- tions in A ( D ) is a weak Cauchy sequence ( a sequence ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ