Linear Operators: General theory |
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Page 46
... obtained from ( a ,, ) by retaining only the elements to the i , . . . , i , th rows and the j1 , ... , j , th columns , and let B ( i̟ , . ipi i ... , ip ) denote the determinant of b ( i , ... , ipi i , ... , ip ) . Then the cofactor ...
... obtained from ( a ,, ) by retaining only the elements to the i , . . . , i , th rows and the j1 , ... , j , th columns , and let B ( i̟ , . ipi i ... , ip ) denote the determinant of b ( i , ... , ipi i , ... , ip ) . Then the cofactor ...
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 395
... obtained in which there may be linear relations between the values of the functions at pairs of points . The following result is also due to Kakutani . THEOREM . The conjugate space of an abstract M - space is an ab- stract L - space ...
... obtained in which there may be linear relations between the values of the functions at pairs of points . The following result is also due to Kakutani . THEOREM . The conjugate space of an abstract M - space is an ab- stract L - space ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ