Linear Operators: General theory |
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Page 204
... zero and since 0 ≤ fn ( 8a , ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point in S , for which fn ( s ) is defined for all n and for which the se- quence { f ( s ) } does not converge to zero ...
... zero and since 0 ≤ fn ( 8a , ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point in S , for which fn ( s ) is defined for all n and for which the se- quence { f ( s ) } does not converge to zero ...
Page 452
... zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is not ... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if f is a non - zero ...
... zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is not ... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if f is a non - zero ...
Page 595
... zero in the weak operator topology . Suppose that { ƒ „ ( T ) x } is weakly se- quentially compact for each x in X ... zero a in X2 , the sequence { fn ( T ) } converges to a non - zero element of X2 . Since f ( T ) commutes with R ( 2 ...
... zero in the weak operator topology . Suppose that { ƒ „ ( T ) x } is weakly se- quentially compact for each x in X ... zero a in X2 , the sequence { fn ( T ) } converges to a non - zero element of X2 . Since f ( T ) commutes with R ( 2 ...
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