Linear Operators: General theory |
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Page 464
... satisfies also satisfies for some xo € K. inf Rf ( x ) RP ( f ) ≤ sup Rf ( x ) , P ( ƒ ) = f ( x 。) , fer ( 4 ) Iƒ K ¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of T - closed convex sets , all ...
... satisfies also satisfies for some xo € K. inf Rf ( x ) RP ( f ) ≤ sup Rf ( x ) , P ( ƒ ) = f ( x 。) , fer ( 4 ) Iƒ K ¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of T - closed convex sets , all ...
Page 498
... satisfies ( i ) then ( ii ) defines an operator Ton X to L ( S , E , μ ) whose norm satisfies ( iii ) . Furthermore T is weakly compact if and only if x * ( · ) is countably additive on in the strong topology of X * . PROOF . If , for E ...
... satisfies ( i ) then ( ii ) defines an operator Ton X to L ( S , E , μ ) whose norm satisfies ( iii ) . Furthermore T is weakly compact if and only if x * ( · ) is countably additive on in the strong topology of X * . PROOF . If , for E ...
Page 557
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where ß ; min ( x ,, v ( ¿ ¿ ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order ( 2 ) at each λ e o ( T ) is divisible by R ...
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where ß ; min ( x ,, v ( ¿ ¿ ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order ( 2 ) at each λ e o ( T ) is divisible by R ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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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 Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ