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Page 72
... subspace of a B - space X , the mapping a * →→ ̄ * 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 * →→ ̄ * 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 420
... subspace of Y * , then each element y € Y determines the linear functional ƒ , on X defined by f ( x ) = x ( y ) , x € X , บ and the subspace I fye Y } X is obviously total . The I to- pology of X is often called the topology of X. It ...
... subspace of Y * , then each element y € Y determines the linear functional ƒ , on X defined by f ( x ) = x ( y ) , x € X , บ and the subspace I fye Y } X is obviously total . The I to- pology of X is often called the topology of X. It ...
Page 436
... subspace of X. Show that the ** topology of X , is the same as the relative * topology of X. 7 Let X be a linear space , and I a total subspace of X * . Show that a set AX is П - bounded if and only if f ( A ) is a bounded set of ...
... subspace of X. Show that the ** topology of X , is the same as the relative * topology of X. 7 Let X be a linear space , and I a total subspace of X * . Show that a set AX is П - bounded if and only if f ( A ) is a bounded set of ...
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