Linear Operators: General theory |
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Page 473
... uniform convexity in the neighborhood of a point implies uniform convexity , and ( Day [ 4 , 6 ] ) demonstrated that under certain conditions combinations also yield uniformly convex spaces . A dual notion of " uniform flattening " is ...
... uniform convexity in the neighborhood of a point implies uniform convexity , and ( Day [ 4 , 6 ] ) demonstrated that under certain conditions combinations also yield uniformly convex spaces . A dual notion of " uniform flattening " is ...
Page 841
... uniform continuity , I.6.16-18 ( 23- 24 ) of almost periodic functions , IV.7.4 ( 283 ) Continuous ( or μ ... uniform , definition , IV.6.10 ( 268 ) properties , IV.6.11-12 ( 268-269 ) , IV.6.30-31 ( 281 ) μ - uniform , criteria for ...
... uniform continuity , I.6.16-18 ( 23- 24 ) of almost periodic functions , IV.7.4 ( 283 ) Continuous ( or μ ... uniform , definition , IV.6.10 ( 268 ) properties , IV.6.11-12 ( 268-269 ) , IV.6.30-31 ( 281 ) μ - uniform , criteria for ...
Page 857
... Uniform boundedness principle , in B - spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost periodic function , IV.7.4 ( 283 ) criterion for ...
... Uniform boundedness principle , in B - spaces , II.3.20-21 ( 66 ) discussion of , ( 80-82 ) in F - spaces , II.1.11 ( 52 ) for measures , IV.9.8 ( 309 ) Uniform continuity , of an almost periodic function , IV.7.4 ( 283 ) criterion for ...
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