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Page 373
... Riesz [ 2 ; p . 456 ] . Lemma 4.2 is due to F. Riesz [ 8 ; p . 36 ] and was also used by Sz . - Nagy [ 5 ] . A similar argument may be applied to obtain this result in any uniformly convex B - space . This generalizes and abstracts a ...
... Riesz [ 2 ; p . 456 ] . Lemma 4.2 is due to F. Riesz [ 8 ; p . 36 ] and was also used by Sz . - Nagy [ 5 ] . A similar argument may be applied to obtain this result in any uniformly convex B - space . This generalizes and abstracts a ...
Page 608
... Riesz who most fully revealed and developed it along the lines presented here . The reader of his book ( F. Riesz [ 3 ] , particularly Secs . 71-82 ) will find many of these concepts and results exposed with an approach that is strik ...
... Riesz who most fully revealed and developed it along the lines presented here . The reader of his book ( F. Riesz [ 3 ] , particularly Secs . 71-82 ) will find many of these concepts and results exposed with an approach that is strik ...
Page 729
... Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its adjoint , was given by Riesz and Sz . - Nagy [ 2 ] . Theorems for abstract vector ...
... Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for a contraction in Hilbert space is also a fixed point for its adjoint , was given by Riesz and Sz . - Nagy [ 2 ] . Theorems for abstract vector ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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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