Linear Operators: General theory |
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Page 449
... non - zero tangent functional at each point of a dense subset of its boundary . Then A is convex . PROOF . Denoting the interior of A by A1 , we will show first that there is no non - zero tangent to A at any point of aД1 + ( 1 — a ) A ...
... non - zero tangent functional at each point of a dense subset of its boundary . Then A is convex . PROOF . Denoting the interior of A by A1 , we will show first that there is no non - zero tangent to A at any point of aД1 + ( 1 — a ) A ...
Page 452
... non- zero continuous linear functional tangent to K at p . If A is a subset of X , and P 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 P 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 ; = 0 . If R S1 S2S , then R ( T ) ; = 0 , and consequently R ( T ) x = 0 for all x € X. Thus a non - zero polynomial R exists such that R ( T ) - • i - = 0 . Let R be ...
... non - zero polynomials S , i = 2 , . . . , k such that S , ( T ) x ; = 0 . If R S1 S2S , then R ( T ) ; = 0 , and consequently R ( T ) x = 0 for all x € X. Thus a non - zero polynomial R exists such that R ( T ) - • i - = 0 . Let R be ...
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