Linear Operators: General theory |
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Page 584
... uniform topology of operators . Then f , converges uniformly on σ ( T ) . 33 Let U be an open set in the complex plane . Suppose that f ( 2 , · ) € F ( T ) for each λ € U and that f ( λ , T ) is an analytic function with values in B ( X ) ...
... uniform topology of operators . Then f , converges uniformly on σ ( T ) . 33 Let U be an open set in the complex plane . Suppose that f ( 2 , · ) € F ( T ) for each λ € U and that f ( λ , T ) is an analytic function with values in B ( X ) ...
Page 594
... uniform topo- logy of operators . It follows from [ * ] that { ƒ „ ( T ) } will converge in the uniform topology if { f ( m ) ( 2 ; ) } converges for m < v1 , 1 ≤ i ≤ k . Since via , the theorem is proved . Q.E.D. 2 ***** COROLLARY ...
... uniform topo- logy of operators . It follows from [ * ] that { ƒ „ ( T ) } will converge in the uniform topology if { f ( m ) ( 2 ; ) } converges for m < v1 , 1 ≤ i ≤ k . Since via , the theorem is proved . Q.E.D. 2 ***** COROLLARY ...
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
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ