Linear Operators: General theory |
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Page 82
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
... give a very simple proof of the uniform boundedness theorem for B - spaces . Bourbaki [ 3 ] has demonstrated that Theorem 1.17 remains valid in a certain class of locally convex topological linear spaces . ( See also Dieudonné and ...
Page 337
... give answers valid for the space BV ( I ) to many other of the ques- tions asked in Section 1. We leave the details to the reader as an exer- cise . It was shown in Chapter III.5 ( cf. the discussion following Lemma III.5.16 ) that if ƒ ...
... give answers valid for the space BV ( I ) to many other of the ques- tions asked in Section 1. We leave the details to the reader as an exer- cise . It was shown in Chapter III.5 ( cf. the discussion following Lemma III.5.16 ) that if ƒ ...
Page 728
... give an extended account or bibliography of this theory . However , we do wish to make a few observations that may be found of interest , restricting our discussion to the material discussed in the text . Mean ergodic theorem . The ...
... give an extended account or bibliography of this theory . However , we do wish to make a few observations that may be found of interest , restricting our discussion to the material discussed in the text . Mean ergodic theorem . The ...
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