Linear Operators: General theory |
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Page 237
... Problem . What is an analytical representation of the conjugate space of the given space X ? 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 n Problem . When does a ...
... Problem . What is an analytical representation of the conjugate space of the given space X ? 1 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 n Problem . When does a ...
Page 407
... problem . a 1 მ 2 [ t ] F ( x , t ) - at 4 dx2 F ( x , t ) + V ( x , t ) F ( x , t ) , t 0 ; F ( x , 0 ) = f ( x ) , V being a given coefficient function . This formula is [ †† ] _F ( x , t ) = √¿f ( q ( t ) + x ) exp { ! ' V ( t − s ...
... problem . a 1 მ 2 [ t ] F ( x , t ) - at 4 dx2 F ( x , t ) + V ( x , t ) F ( x , t ) , t 0 ; F ( x , 0 ) = f ( x ) , V being a given coefficient function . This formula is [ †† ] _F ( x , t ) = √¿f ( q ( t ) + x ) exp { ! ' V ( t − s ...
Page 613
... problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations . ( i ) = T ( t + u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u ≥ 0 . An operator valued function T ( t ) ...
... problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations . ( i ) = T ( t + u ) = T ( t ) T ( u ) , T ( 0 ) = 1 , t , u ≥ 0 . An operator valued function T ( t ) ...
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