Linear Operators: General theory |
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Page 46
... indices 1 ≤ < < in . Similarly , det ( a ,; ) may be calculated in terms of ele- ments of the 1 , ... , jpth columns by summing over all sets of p indices 1≤į < ... < i , ≤ n . In case p = 1 the Laplace expansion reduces to the ...
... indices 1 ≤ < < in . Similarly , det ( a ,; ) may be calculated in terms of ele- ments of the 1 , ... , jpth columns by summing over all sets of p indices 1≤į < ... < 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 41 ...
... 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 41 ...
Page 467
... indices , and where fa , and fa , are omitted from the enumeration . Clear- ly C11 = C'j ;, and by the laws governing differentiation of determinants and interchange of columns in them we have Σ ( -1 ) Cu + Σ ( -1 ) -1C . j < i a D მე ...
... indices , and where fa , and fa , are omitted from the enumeration . Clear- ly C11 = C'j ;, and by the laws governing differentiation of determinants and interchange of columns in them we have Σ ( -1 ) Cu + Σ ( -1 ) -1C . j < i a D მე ...
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