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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian 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