Linear Operators: General theory |
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Page xvi
... union , or sum , of the sets a in A. This union is denoted by A or Ua . The intersection , or product , of the sets a in A is the set of all in A which are elements of every a e A. If A = { a , b , . . . , c } we will sometimes write the ...
... union , or sum , of the sets a in A. This union is denoted by A or Ua . The intersection , or product , of the sets a in A is the set of all in A which are elements of every a e A. If A = { a , b , . . . , c } we will sometimes write the ...
Page 2
... union , or sum , of the sets a in A. This union is denoted by ○ A or Ua . The intersection , or product , of the sets a in A is the set of all x in A which are elements of every a e A. If A { a , b , . . . , c } we will sometimes write ...
... union , or sum , of the sets a in A. This union is denoted by ○ A or Ua . The intersection , or product , of the sets a in A is the set of all x in A which are elements of every a e A. If A { a , b , . . . , c } we will sometimes write ...
Page 10
... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , 7 ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If τ , t1 ...
... union of every one of its subfamilies , and the intersection of every one of its finite subfamilies . The pair ( X , 7 ) is called a topological space ; but sometimes ift is understood , we refer to X as a topological space . If τ , t1 ...
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