Linear Operators: General theory |
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Page 263
... arbitrary open set containing F1 - G1 we have μ1 ( F1 ) ≤λ ( G1 ) + μ1 ( F1 — G1 ) . If F is a closed set it ... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ1⁄2 ...
... arbitrary open set containing F1 - G1 we have μ1 ( F1 ) ≤λ ( G1 ) + μ1 ( F1 — G1 ) . If F is a closed set it ... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ1⁄2 ...
Page 269
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ1⁄2 ( E ) ≤ μ1⁄2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary ...
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ1⁄2 ( E ) ≤ μ1⁄2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary ...
Page 476
... arbitrary finite subset of X , and ε > 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 ε > 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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ