Linear Operators: General theory |
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Page 263
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ2 ( E ) ≤ μ2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary closed ...
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ2 ( E ) ≤ μ2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary closed ...
Page 281
... arbitrary set . A sequence { f } in B ( S ) converges weakly to fo if and only if it is bounded and , together with ... arbitrary complex numbers and 1 , ... , λ , are arbitrary real numbers . In other words , the theory gives an ...
... arbitrary set . A sequence { f } in B ( S ) converges weakly to fo if and only if it is bounded and , together with ... arbitrary complex numbers and 1 , ... , λ , are arbitrary real numbers . In other words , the theory gives an ...
Page 476
... arbitrary finite subset of X , and ɛ > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { T } converges to T if and only if { T } converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in B ...
... arbitrary finite subset of X , and ɛ > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { T } converges to T if and only if { T } converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in B ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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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