Linear Operators: General theory |
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Page 22
... finite number of a Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a ... G .... contains a finite subcovering . If U G , A , let Xn & Un = 1 Gi , Xn € A. Let xn¡ → be a convergent subsequence ...
... finite number of a Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a ... G .... contains a finite subcovering . If U G , A , let Xn & Un = 1 Gi , Xn € A. Let xn¡ → be a convergent subsequence ...
Page 43
... finite set { 1 ,. n } CA , then H ( x ) ‡ þ . If B1 is the set of all finite products of elements in A1 , then B1 ... G is any set in H which is both open and closed in H , then since G is open we have G UH ( x ) . Since G is compact , a ...
... finite set { 1 ,. n } CA , then H ( x ) ‡ þ . If B1 is the set of all finite products of elements in A1 , then B1 ... G is any set in H which is both open and closed in H , then since G is open we have G UH ( x ) . Since G is compact , a ...
Page 454
... G = { g } , if for each fe F and ɛ > 0 , there exists a neighborhood N ( 0 ; 7 , 8 ) = { x || g ( x ) | < d , gey } , where y is a finite subset of G , with the property that if p , qe K and p −9 € N ( 0 ; 7,8 ) , then f ( Tp ) -f ( Tq ) ...
... G = { g } , if for each fe F and ɛ > 0 , there exists a neighborhood N ( 0 ; 7 , 8 ) = { x || g ( x ) | < d , gey } , where y is a finite subset of G , with the property that if p , qe K and p −9 € N ( 0 ; 7,8 ) , then f ( Tp ) -f ( Tq ) ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ