Linear Operators: General theory |
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Page 72
... subspace of a B - space X , the mapping a * → ã * where * 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 , show ...
... subspace of a B - space X , the mapping a * → ã * where * 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 , show ...
Page 436
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X. Let X be a linear space , and I a total subspace of X. Show that a set AX is T - bounded if and only if f ( A ) is a bounded set of scalars ...
... subspace of X. Show that the ** topology of X , is the same as the relative X * topology of X. Let X be a linear space , and I a total subspace of X. Show that a set AX is T - bounded if and only if f ( A ) is a bounded set of scalars ...
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 is closed . -- 17 Let be a B - space and suppose that ...
... 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 is closed . -- 17 Let be a B - space and suppose that ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ