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 2 , . . . , 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 2 , . . . , 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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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