Linear Operators: General theory |
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Page 490
... operators with range in C ( S ) and then operators defined on C ( S ) . 1 THEOREM . Let S be a compact Hausdorff space and let T be a bounded linear operator from a B - space X into C ( S ) . Then there exists a mapping : S → X * which ...
... operators with range in C ( S ) and then operators defined on C ( S ) . 1 THEOREM . Let S be a compact Hausdorff space and let T be a bounded linear operator from a B - space X into C ( S ) . Then there exists a mapping : S → X * which ...
Page 494
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rea ( S ) , and ...
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rea ( S ) , and ...
Page 581
... operator . = 7 Let T be the map in l ,, 1 ≤ p ≤∞o , defined by T [ §1 , §2 , . . . ] [ $ 2,3 , ... ] . Find o , ( T ) , o , ( T ) , o . ( T ) . 8 If E is a projection operator , find the resolvent R ( 2 ; E ) ex- plicitly in terms of ...
... operator . = 7 Let T be the map in l ,, 1 ≤ p ≤∞o , defined by T [ §1 , §2 , . . . ] [ $ 2,3 , ... ] . Find o , ( T ) , o , ( T ) , o . ( T ) . 8 If E is a projection operator , find the resolvent R ( 2 ; E ) ex- plicitly in terms of ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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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