Linear Operators: General theory |
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Page 213
... satisfies μ ( S ( C , 38 ( C ) ) ) ≤ ( 6√ / n + 1 ) " μ ( C ) , it follows that covers A in the sense of Vitali . Hence by Theorem 3 there is a sequence of closed cubes { C } such that A- UC is a μ - null set . For each k let De be ...
... satisfies μ ( S ( C , 38 ( C ) ) ) ≤ ( 6√ / n + 1 ) " μ ( C ) , it follows that covers A in the sense of Vitali . Hence by Theorem 3 there is a sequence of closed cubes { C } such that A- UC is a μ - null set . For each k let De be ...
Page 464
... satisfies inf Rf ( x ) ≤ RÞ ( f ) ≤ sup Rf ( x ) , TEK also satisfies P ( ƒ ) = f ( xo ) , x € K je ľ je ľ for some x K. ( 4 ) If K¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of T - closed convex ...
... satisfies inf Rf ( x ) ≤ RÞ ( f ) ≤ sup Rf ( x ) , TEK also satisfies P ( ƒ ) = f ( xo ) , x € K je ľ je ľ for some x K. ( 4 ) If K¿ , § < 0 , 0 a limit ordinal , is a monotone decreasing trans- finite sequence of T - closed convex ...
Page 557
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where Bi min ( α¿ , v ( ^ ¿ ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order v ( 2 ) at each λ e σ ( T ) is divisible by R2 ...
... satisfies R1 ( T ) = 0. In the same way , the product R2 of all the factors ( 2-2 ) , where Bi min ( α¿ , v ( ^ ¿ ) ) , satisfies R2 ( T ) = 0. Since any polynomial P having a zero of order v ( 2 ) at each λ e σ ( T ) is divisible by R2 ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ