Linear Operators: General theory |
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Page 380
... results . Riesz announced his result in 1909 ( F. Riesz [ 7 ] ) . Since then he has given several different proofs of this result ( Riesz [ 3 , 10 , 11 ] ) . Another proof , still for C [ 0 , 1 ] was supplied by Helly [ 1 ] . Radon [ 2 ...
... results . Riesz announced his result in 1909 ( F. Riesz [ 7 ] ) . Since then he has given several different proofs of this result ( Riesz [ 3 , 10 , 11 ] ) . Another proof , still for C [ 0 , 1 ] was supplied by Helly [ 1 ] . Radon [ 2 ...
Page 388
... results to a certain class of functions closely related to L1 , but which do not form a B - space . The reader is referred to his paper for the details . Corollary 8.13 is a classical result due to Schur [ 1 ] . There is a similar ...
... results to a certain class of functions closely related to L1 , but which do not form a B - space . The reader is referred to his paper for the details . Corollary 8.13 is a classical result due to Schur [ 1 ] . There is a similar ...
Page 390
... result is proved . ( For other results related to the atomic struc- ture of a measure space , see Hahn and Rosenthal [ 1 ; pp.45-53 ] and Halmos [ 5 ; pp . 165-174 ] . ) Theorem 9.14 is due to Bochner [ 3 ] . Bochner and Phillips [ 1 ] ...
... result is proved . ( For other results related to the atomic struc- ture of a measure space , see Hahn and Rosenthal [ 1 ; pp.45-53 ] and Halmos [ 5 ; pp . 165-174 ] . ) Theorem 9.14 is due to Bochner [ 3 ] . Bochner and Phillips [ 1 ] ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ