Linear Operators: General theory |
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Page 12
... closure of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show that p , Xe F , and 10 ( a ) shows that A ○ Be F if A , B e F. It follows that any finite union of sets in F is in F. From 10 ( a ) , it follows that AC B implies ...
... closure of A in this topology . PROOF . Statements 10 ( b ) , ( d ) show that p , Xe F , and 10 ( a ) shows that A ○ Be F if A , B e F. It follows that any finite union of sets in F is in F. From 10 ( a ) , it follows that AC B implies ...
Page 462
... closure for subspaces of a normed linear space ( a special case of Theorem 3.13 ) appears in Banach 1 ; pp . 58 ... closure which we have studied , various special definitions of closure for subspaces or convex subsets of a linear ...
... closure for subspaces of a normed linear space ( a special case of Theorem 3.13 ) appears in Banach 1 ; pp . 58 ... closure which we have studied , various special definitions of closure for subspaces or convex subsets of a linear ...
Page 511
... closure of co ( 4 ) . If A is compact in the strong operator topology , so is the strong operator closure of co ( 4 ) . 4 If a set AC B ( X , Y ) is sequentially compact in the weak operator topology , its weak operator closure is ...
... closure of co ( 4 ) . If A is compact in the strong operator topology , so is the strong operator closure of co ( 4 ) . 4 If a set AC B ( X , Y ) is sequentially compact in the weak operator topology , its weak operator closure is ...
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 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