Linear Operators: General theory |
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Page 7
... shown that it is well - ordered and hence belongs to & . The statement x ≤'x for x e UE is clear . If x ≤'y and y ≤'z , then x , y € E。€ 80 , y , z € E1 € ε 0 , x ≤oy , and y ≤ z . Since & is totally ordered it may be supposed ...
... shown that it is well - ordered and hence belongs to & . The statement x ≤'x for x e UE is clear . If x ≤'y and y ≤'z , then x , y € E。€ 80 , y , z € E1 € ε 0 , x ≤oy , and y ≤ z . Since & is totally ordered it may be supposed ...
Page 335
... shown that W satisfies the hypothesis of Zorn's lemma . To do this we let Wo be a totally ordered subset of W ( I.22 ) and let c CUW 。· Then , for some a e Wo , ca is not void . Let x be the smallest element of ca and let y be any ...
... shown that W satisfies the hypothesis of Zorn's lemma . To do this we let Wo be a totally ordered subset of W ( I.22 ) and let c CUW 。· Then , for some a e Wo , ca is not void . Let x be the smallest element of ca and let y be any ...
Page 553
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and Pcoin- cide . This is not the ...
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and Pcoin- cide . This is not the ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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 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