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 { fn } in B ( S ) converges weakly to fo if and only if it is bounded and , together with ... arbitrary complex numbers and 2 , ... , 2. , are arbitrary real numbers . In other words , the theory gives an ...
... arbitrary set . A sequence { fn } in B ( S ) converges weakly to fo if and only if it is bounded and , together with ... arbitrary complex numbers and 2 , ... , 2. , 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 |
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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