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 calculating ...
... 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 calculating ...
Page 233
... obtained by Phillips [ 7 ] and Rickart [ 1 ] . All of these inte- grals are countably additive integrals . In Section IV.10 we will pre- sent a Lebesgue type theory of integration of a scalar function with respect to a countably ...
... obtained by Phillips [ 7 ] and Rickart [ 1 ] . All of these inte- grals are countably additive integrals . In Section IV.10 we will pre- sent a Lebesgue type theory of integration of a scalar function with respect to a countably ...
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 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ