Linear Operators: General theory |
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Page 72
... subspace of a B - space X , the mapping a * → * where a * 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 a * 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 e Y determines the linear functional ƒ , on X defined by f ( x ) = x ( y ) , x ε X , บ บ and the subspace г = { ƒ „ \ y € Y } CX is obviously total . The ľ to- pology of X is often called the Y ...
... subspace of Y * , then each element y e Y determines the linear functional ƒ , on X defined by f ( x ) = x ( y ) , x ε X , บ บ and the subspace г = { ƒ „ \ y € Y } CX is obviously total . The ľ to- pology of X is often called the Y ...
Page 436
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X. 7 Let X be a linear space , and I a total subspace of X * . Show that a set ACX is T - bounded if and only if f ( 4 ) is a bounded set of ...
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X. 7 Let X be a linear space , and I a total subspace of X * . Show that a set ACX is T - bounded if and only if f ( 4 ) is a bounded set of ...
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