Linear Operators: General theory |
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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 ( ɛ ) ≤ T ( 8 ) if ɛ < § and that -t e T ( ɛ ) whenever t e T ( ɛ ) . The function f is said to be almost periodic if it is continuous and if for every ɛ > 0 there is an L L ( ɛ ) > 0 such that every interval in R of ...
... clear that T ( ɛ ) ≤ T ( 8 ) if ɛ < § and that -t e T ( ɛ ) whenever t e T ( ɛ ) . The function f is said to be almost periodic if it is continuous and if for every ɛ > 0 there is an L L ( ɛ ) > 0 such that every interval in R of ...
Page 292
... clear that if F1 and F2 are elements of Σ , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 € 23 , and that if F1 , F2 € Σ3 with F1F2 = 0 , then F1 ○ F2 € Σ3 . It follows that Σ is a field . If { F } is a sequence of ...
... clear that if F1 and F2 are elements of Σ , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 € 23 , and that if F1 , F2 € Σ3 with F1F2 = 0 , then F1 ○ F2 € Σ3 . It follows that Σ is a field . If { F } is a sequence of ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 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