Linear Operators: General theory |
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Page 464
... satisfies also satisfies inf Rf ( x ) RP ( f ) ≤ sup Rf ( x ) , P ( f ) = f ( x 。) , TEK fer jε T for some xe K. ( 4 ) Iƒ K¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of l - closed convex sets , all ...
... satisfies also satisfies inf Rf ( x ) RP ( f ) ≤ sup Rf ( x ) , P ( f ) = f ( x 。) , TEK fer jε T for some xe K. ( 4 ) Iƒ K¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of l - closed convex sets , all ...
Page 498
... satisfies ( i ) then ( ii ) defines an operator Ton X to L1 ( S , Σ , 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 ...
... satisfies ( i ) then ( ii ) defines an operator Ton X to L1 ( S , Σ , 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 ...
Page 557
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where B min ( ¤¿ , v ( 2 ; ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order v ( 2 ) at each λ € σ ( T ) is divisible by R2 ...
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where B min ( ¤¿ , v ( 2 ; ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order v ( 2 ) at each λ € σ ( T ) is divisible by R2 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ