Linear Operators: General theory |
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Page 452
... non- zero continuous linear functional tangent to K at p . If A is a subset of X , and Ρ is in A , then there exists a non - zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is ...
... non- zero continuous linear functional tangent to K at p . If A is a subset of X , and Ρ is in A , then there exists a non - zero continuous linear functional tangent to A at p if and only if the cone B with vertex p generated by A is ...
Page 557
... non - zero polynomials S , i = 2 , . . . , k such that S , ( T ) x If R S1 S2S , then R ( T ) x = 0 , and consequently R ( T ) = 0 for all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored as R ( 2 ) BIT1 ...
... non - zero polynomials S , i = 2 , . . . , k such that S , ( T ) x If R S1 S2S , then R ( T ) x = 0 , and consequently R ( T ) = 0 for all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored as R ( 2 ) BIT1 ...
Page 579
... non - zero number in o ( T ) is a pole of T and has finite positive index . For such a number 2 , the projection E ( 2 ) has a non - zero finite dimensional range given by the formula E ( 2 ) X = { x | ( T — λI ) x = 0 } where v is the ...
... non - zero number in o ( T ) is a pole of T and has finite positive index . For such a number 2 , the projection E ( 2 ) has a non - zero finite dimensional range given by the formula E ( 2 ) X = { x | ( T — λI ) x = 0 } where v is the ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ