Linear Operators: General theory |
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Page 269
... 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 ε < 8 and that ―te T ( E ) whenever t e T ( ɛ ) . The function f is said to be almost periodic if it is continuous and if for every ε > 0 there is an L L ( e ) > 0 such that every interval in R of length L ...
... clear that T ( e ) CT ( 8 ) if ε < 8 and that ―te T ( E ) whenever t e T ( ɛ ) . The function f is said to be almost periodic if it is continuous and if for every ε > 0 there is an L L ( e ) > 0 such that every interval in R of length L ...
Page 292
... clear that if F1 and F2 are elements of Σ3 , then F1F2 € 23. It is also clear that if F1 € Σ , then S - F1 € 23 , and that if F1 , F2 € 23 with F1F2 = 6 , then F1 UF2 e 23 . It follows that 3 is a field . If { F } is a sequence of ...
... clear that if F1 and F2 are elements of Σ3 , then F1F2 € 23. It is also clear that if F1 € Σ , then S - F1 € 23 , and that if F1 , F2 € 23 with F1F2 = 6 , then F1 UF2 e 23 . It follows that 3 is a field . If { F } is a sequence of ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ