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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ