Linear Operators: General theory |
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Page vii
... tion have been discussed in the literature . In addition , they contain references to many results related to but not included among those given in the text . In this capacity , the notes and remarks supplement the bibliography on the ...
... tion have been discussed in the literature . In addition , they contain references to many results related to but not included among those given in the text . In this capacity , the notes and remarks supplement the bibliography on the ...
Page 101
... tion defined on a set S and μ a finitely additive set function defined on a field of subsets of S. It will not be assumed that u is bounded . Thus the basis for this material is a fixed set S , a field Σ of subsets of S , and a finitely ...
... tion defined on a set S and μ a finitely additive set function defined on a field of subsets of S. It will not be assumed that u is bounded . Thus the basis for this material is a fixed set S , a field Σ of subsets of S , and a finitely ...
Page 659
... tion ( vi ) . However , in order to explain the main concepts , it is convenient to avoid certain technical difficulties by first treating the discrete case rather than the continuous case . For example , instead of studying a ...
... tion ( vi ) . However , in order to explain the main concepts , it is convenient to avoid certain technical difficulties by first treating the discrete case rather than the continuous case . For example , instead of studying 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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ