Linear Operators: General theory |
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Page 388
... given by Phillips [ 3 ; p . 527 ] . A different criterion was given for L ,, p≥ 1 , by Fréchet [ 7 ] . Nicolescu [ 1 ] has also discussed the Kolmogoroff result . Conditions of the type introduced by Kolmo- goroff were employed by ...
... given by Phillips [ 3 ; p . 527 ] . A different criterion was given for L ,, p≥ 1 , by Fréchet [ 7 ] . Nicolescu [ 1 ] has also discussed the Kolmogoroff result . Conditions of the type introduced by Kolmo- goroff were employed by ...
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 ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ