Linear Operators: General theory |
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Page 72
... subspace of a B - space X , the mapping a * → ã * where * is defined by * ( x + 3 ) = x * ( x ) , is an isometric isomorphism of 3 onto all of ( X / 3 ) * . ( c ) If X is a reflective B - space and 3 is a closed subspace of X , show ...
... subspace of a B - space X , the mapping a * → ã * where * is defined by * ( x + 3 ) = x * ( x ) , is an isometric isomorphism of 3 onto all of ( X / 3 ) * . ( c ) If X is a reflective B - space and 3 is a closed subspace of X , show ...
Page 311
... subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such ... subspace of the space of countably additive measures on the Borel sets in S1 , is weakly com- plete by Theorem 4 ...
... subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such ... subspace of the space of countably additive measures on the Borel sets in S1 , is weakly com- plete by Theorem 4 ...
Page 420
... subspace of Y * , then each element y e determines the linear functional f , on X defined by f ( x ) = x ( y ) , x € X , and the subspace I = fye Y } CX is obviously total . The I to- pology of X is often called the Y topology of X. It ...
... subspace of Y * , then each element y e determines the linear functional f , on X defined by f ( x ) = x ( y ) , x € X , and the subspace I = fye Y } CX is obviously total . The I to- pology of X is often called the Y topology of X. It ...
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