Linear Operators: General theory |
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Page 72
... subspace of a B - space X , the mapping a * → x * 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 * → x * 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 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 П to- pology of X is often called the 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 П to- pology of X is often called the topology of X. It ...
Page 513
... subspace of a B - space and N is a finite di- mensional subspace , then N is a closed subspace . If N is a closed subspace , and N is finite dimensional , it does not follow that Y is closed . 17 Let X be a B - space and suppose that X ...
... subspace of a B - space and N is a finite di- mensional subspace , then N is a closed subspace . If N is a closed subspace , and N is finite dimensional , it does not follow that Y is closed . 17 Let X be a B - space and suppose that X ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ