Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 89
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
... B - algebras . Completion of spaces . In the definitions of F- and B - spaces , we required the spaces to be ... space satisfying properties ( i ) and ( ii ) of Definition 1.10 . Then X is isomorphic and isometric with a dense linear subspace ...
Page 258
... B - space , suppose that { f } is a Cauchy sequence in B ( S ) . Then for each ɛ > 0 there is an m ( ɛ ) with | fn − fm | < ε for n , mm ( ε ) . Let f ( s ) = lim , fn ( s ) for each s in S. For each s in S there is a p≥m ( ɛ ) with ...
... B - space , suppose that { f } is a Cauchy sequence in B ( S ) . Then for each ɛ > 0 there is an m ( ɛ ) with | fn − fm | < ε for n , mm ( ε ) . Let f ( s ) = lim , fn ( s ) for each s in S. For each s in S there is a p≥m ( ɛ ) with ...
Page 398
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in * is actually ** - convergent , and that if Y is a separable B - space , then any ...
... space . Let S be a Stone space and X C ( S ) the real continuous func- tions . Grothendieck [ 4 ; p . 168 ] showed that every X - convergent se- quence in * is actually ** - convergent , and that if Y is a separable B - space , then any ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
49 other sections not shown
Other editions - View all
Common terms and phrases
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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ