Linear Operators: General theory |
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Page 419
... topology of X is the topology obtained by taking as base all sets of the form . N ( p ; A , ε ) = { q || f ( p ) −ƒ ( q ) | < ɛ , † € A } , where pe X , A is a finite subset of I ... topology if and only if lim , x V.3.2 419 WEAK TOPOLOGIES.
... topology of X is the topology obtained by taking as base all sets of the form . N ( p ; A , ε ) = { q || f ( p ) −ƒ ( q ) | < ɛ , † € A } , where pe X , A is a finite subset of I ... topology if and only if lim , x V.3.2 419 WEAK TOPOLOGIES.
Page 420
... topological space and X = Y * . In this case , what is known as the Y topology of Y * is ob- tained . - The reader will have observed that in certain cases a number of different topologies have been defined for the same space X. For in ...
... topological space and X = Y * . In this case , what is known as the Y topology of Y * is ob- tained . - The reader will have observed that in certain cases a number of different topologies have been defined for the same space X. For in ...
Page 477
... topology , and that the strong operator topology is stronger than the weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the ...
... topology , and that the strong operator topology is stronger than the weak operator topology . With its uniform operator topology , B ( X , Y ) becomes a B - space ; as such , it has a weak topology which should not be confused with the ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ