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 598
... uniform operator topology , then there exists a spectral subset o1 of o ( T ) such that E = E ( 01 ) . ( Hint . See Exercise VII.5.32 . ) n 4 Let Te B ( X ) , T2 e B ( X ) , n = 1 , 2 , . . .. Suppose that T → T in the uniform topology ...
... uniform operator topology , then there exists a spectral subset o1 of o ( T ) such that E = E ( 01 ) . ( Hint . See Exercise VII.5.32 . ) n 4 Let Te B ( X ) , T2 e B ( X ) , n = 1 , 2 , . . .. Suppose that T → T in the uniform topology ...
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
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ