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 ) С T ( d ) 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 ɛ > 0 there is an L L ( E ) > 0 such that every interval in R of length ...
... clear that T ( ɛ ) С T ( d ) 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 ɛ > 0 there is an L L ( E ) > 0 such that every interval in R of length ...
Page 292
... clear that if F1 and F2 are elements of £ 3 , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 23 , and that if F1 , F2 € Σ3 with F1F2 = 4 , then F1 ○ F2 € Σ3 . It follows that E , is a field . If { F } is a sequence of ...
... clear that if F1 and F2 are elements of £ 3 , then F1F2 € 23. It is also clear that if F1 € 23 , then S - F1 23 , and that if F1 , F2 € Σ3 with F1F2 = 4 , then F1 ○ F2 € Σ3 . It follows that E , is a field . If { F } is a sequence of ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 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