Linear Operators: General theory |
From inside the book
Results 1-3 of 67
Page 311
... isomorphism of B ( S , Σ ) with C ( S1 ) where S1 is a particular compact Hausdorff space . We shall now investigate what properties the existence of this isomorphism implies for S , and investigate in more detail the isomorphism of ba ...
... isomorphism of B ( S , Σ ) with C ( S1 ) where S1 is a particular compact Hausdorff space . We shall now investigate what properties the existence of this isomorphism implies for S , and investigate in more detail the isomorphism of ba ...
Page 312
... isomorphic with C ( S1 ) . Then the space S1 is uniquely de- termined to within a homeomorphism and is totally disconnected . The correspondence LE → XE , establishes an isomorphism t of the field onto Σ the field of all open and ...
... isomorphic with C ( S1 ) . Then the space S1 is uniquely de- termined to within a homeomorphism and is totally disconnected . The correspondence LE → XE , establishes an isomorphism t of the field onto Σ the field of all open and ...
Page 313
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all Ալ in ba ( S1 , 1 ) . PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the mapping T is ...
... isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all Ալ in ba ( S1 , 1 ) . PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the mapping T is ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 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 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