Linear Operators: General theory |
From inside the book
Results 1-3 of 86
Page 262
... clear that the integral is a continuous linear functional on C ( S ) . The following theorem is a converse to this statement . 2 THEOREM . If S is normal , there is an isometric isomorphism between C * ( S ) and rba ( S ) such that ...
... clear that the integral is a continuous linear functional on C ( S ) . The following theorem is a converse to this statement . 2 THEOREM . If S is normal , there is an isometric isomorphism between C * ( S ) and rba ( S ) such that ...
Page 282
... clear that T ( e ) CT ( 8 ) if ɛ < 8 and that -t e T ( ɛ ) whenever te T ( e ) . The function f is said to be almost periodic if it is continuous and if for every & > 0 there is an L = L ( ɛ ) > 0 such that every interval in R of length ...
... clear that T ( e ) CT ( 8 ) if ɛ < 8 and that -t e T ( ɛ ) whenever te T ( e ) . The function f is said to be almost periodic if it is continuous and if for every & > 0 there is an L = L ( ɛ ) > 0 such that every interval in R of length ...
Page 292
... clear that if F1 and F2 are elements of 23 , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 € 3 , and that if F1 , F2 € Σ3 with F1F2 = 6 , then F1 ○ F2 € £ 3 . It follows that Σ3 is a field . If { F } is a sequence of ...
... clear that if F1 and F2 are elements of 23 , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 € 3 , and that if F1 , F2 € Σ3 with F1F2 = 6 , then F1 ○ F2 € £ 3 . It follows that Σ3 is a field . If { F } is a sequence of ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ