Linear Operators: General theory |
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... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : x a = U ( xa ) , xU ( Na ) = ~ ( xỤ a ) . a € A == ає.1 aε A A ...
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B ... means that the following distributive laws hold : x a = U ( xa ) , xU ( Na ) = ~ ( xỤ a ) . a € A == ає.1 aε A A ...
Page 381
... means of a countably additive measure if and only if any one of the following conditions hold : ( 1 ) fn e C ( S ) , n = 0 , 1 , 2 , . . . and fn ( s ) ↑ fo ( s ) , se S imply that → fo uniformly on S ; ( 2 ) every continuous real ...
... means of a countably additive measure if and only if any one of the following conditions hold : ( 1 ) fn e C ( S ) , n = 0 , 1 , 2 , . . . and fn ( s ) ↑ fo ( s ) , se S imply that → fo uniformly on S ; ( 2 ) every continuous real ...
Page 476
... means the only interesting topologies of B ( X , Y ) . Other topologies in B ( X , Y ) can be introduced in such a way that the convergence of a generalized sequence { T } to a limit T means any one of the following : ( i ) for each a ...
... means the only interesting topologies of B ( X , Y ) . Other topologies in B ( X , Y ) can be introduced in such a way that the convergence of a generalized sequence { T } to a limit T means any one of the following : ( i ) for each a ...
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