Linear Operators: General theory |
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Page 540
... Representation of operators in a Lebesgue space . The form of the representation in Theorem 8.1 for the general operator was given by Kantorovitch and Vulich [ 1 ; p . 138 ] . The bound for norm of the operator was found in the case ...
... Representation of operators in a Lebesgue space . The form of the representation in Theorem 8.1 for the general operator was given by Kantorovitch and Vulich [ 1 ; p . 138 ] . The bound for norm of the operator was found in the case ...
Page 552
... representation of linear operators is that dealing with the representation of linear functions defined on certain spaces with values in a B - space . Gowurin gave a representa- tion for the general bounded linear functional on the space ...
... representation of linear operators is that dealing with the representation of linear functions defined on certain spaces with values in a B - space . Gowurin gave a representa- tion for the general bounded linear functional on the space ...
Page 686
... representation of the vector 4 ( a ) f in L. If we had started with another [ t , s ] -measurable representation K ( t , s ) of T ( t ) f then , since for almost all s , K ( t , s ) = T ( t ) ( f , s ) for almost all t , it is seen that ...
... representation of the vector 4 ( a ) f in L. If we had started with another [ t , s ] -measurable representation K ( t , s ) of T ( t ) f then , since for almost all s , K ( t , s ) = T ( t ) ( f , s ) for almost all t , it is seen that ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ