Linear Operators: General theory |
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Page 72
... subspace of a B - space X , the mapping a * →→ ã * where a * is defined by a * ( 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 ...
... subspace of a B - space X , the mapping a * →→ ã * where a * is defined by a * ( 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 ...
Page 436
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X1 . 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 ( A ) is a bounded set of ...
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X1 . 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 ( A ) is a bounded set of ...
Page 513
... subspace of a B - space and N is a finite di- mensional subspace , then Y N is a closed subspace . If Y N is a closed subspace , and N is finite dimensional , it does not follow that 9 is closed . = 17 Let X be a B - space and suppose ...
... subspace of a B - space and N is a finite di- mensional subspace , then Y N is a closed subspace . If Y N is a closed subspace , and N is finite dimensional , it does not follow that 9 is closed . = 17 Let X be a B - space and suppose ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ