Linear Operators: General theory |
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Page 46
... indices 1 ≤ } ; < < j , ≤n . Similarly , det ( a ,, ) may be calculated in terms of ele- ments of the j j , th columns by summing over all sets of p indices . 1≤4 < ... < i , ≤n . In case p = 1 the Laplace expansion reduces to the ...
... indices 1 ≤ } ; < < j , ≤n . Similarly , det ( a ,, ) may be calculated in terms of ele- ments of the j j , th columns by summing over all sets of p indices . 1≤4 < ... < i , ≤n . In case p = 1 the Laplace expansion reduces to the ...
Page 162
... indices and all finite families of disjoint sets { E } in Σ whose union is E. It will first be shown that μ is additive on E. Let E , F be disjoint sets in Σ and let ɛ > 0 be arbitrary . Let EUF be partitioned into disjoint sets A1 ...
... indices and all finite families of disjoint sets { E } in Σ whose union is E. It will first be shown that μ is additive on E. Let E , F be disjoint sets in Σ and let ɛ > 0 be arbitrary . Let EUF be partitioned into disjoint sets A1 ...
Page 281
... indices corresponding to ε and k = 1 guaranteed by the quasi - uniform convergence of { g } . Then U1 = { $ || gx ̧ ( s ) —fo ( $ ) | > εo } = i - " " r . Since A is dense in S , is an open set containing so for i 1 , there exists a ...
... indices corresponding to ε and k = 1 guaranteed by the quasi - uniform convergence of { g } . Then U1 = { $ || gx ̧ ( s ) —fo ( $ ) | > εo } = i - " " r . Since A is dense in S , is an open set containing so for i 1 , there exists 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