Linear Operators: General theory |
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Page 45
... obtained by deleting the ith row and the jth column in ( a ,, ) . Expressed differ- ently , the cofactor of a ,, is obtained by replacing the element a ,, by 1 and all the other elements of the ith row and jth column by 0 and ...
... obtained by deleting the ith row and the jth column in ( a ,, ) . Expressed differ- ently , the cofactor of a ,, is obtained by replacing the element a ,, by 1 and all the other elements of the ith row and jth column by 0 and ...
Page 387
... obtained by taking the character group Ĝ of G , equipping & with its discrete topology , and then taking the ... obtained by Zaanen [ 1 , 5 ; p . 138 ] . In the case L , [ 0 , 1 ] , 1 < p < ∞ , Corollaries 8.3 and 8.4 were proved by F ...
... obtained by taking the character group Ĝ of G , equipping & with its discrete topology , and then taking the ... obtained by Zaanen [ 1 , 5 ; p . 138 ] . In the case L , [ 0 , 1 ] , 1 < p < ∞ , Corollaries 8.3 and 8.4 were proved by F ...
Page 607
... obtained expansions for the resolvent ( 21 - T ) -1 in the neighborhood of a pole . A special case of Theorem 1.9 is due to Weyr [ 1 ] , and in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1.10 , Frobenius [ 3 ...
... obtained expansions for the resolvent ( 21 - T ) -1 in the neighborhood of a pole . A special case of Theorem 1.9 is due to Weyr [ 1 ] , and in full generality it was proved by Hensel [ 1 ] . In regard to Theorem 1.10 , Frobenius [ 3 ...
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