Linear Operators: General theory |
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Page 392
... given conditions assuring that a sequence of measurable functions has a uniformly convergent sub- sequence . ) Fréchet's arguments were simplified by Hanson [ 1 ] . Some- what different conditions have been given by Izumi [ 2 ] and ...
... given conditions assuring that a sequence of measurable functions has a uniformly convergent sub- sequence . ) Fréchet's arguments were simplified by Hanson [ 1 ] . Some- what different conditions have been given by Izumi [ 2 ] and ...
Page 728
... given here is due to Bade [ 1 ] . Corollary 14 is a result of Widder and Hirschman [ 2 ] . Ergodic theory . Although the development of ergodic theory has taken place principally since 1931 , there is considerable literature on the ...
... given here is due to Bade [ 1 ] . Corollary 14 is a result of Widder and Hirschman [ 2 ] . Ergodic theory . Although the development of ergodic theory has taken place principally since 1931 , there is considerable literature on the ...
Page 729
... given by G. Birkhoff [ 7 ] and F. 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 ] ...
... given by G. Birkhoff [ 7 ] and F. 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 ] ...
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