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 ? 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 Problem . When does a ...
... Problem . What is an analytical representation of the conjugate space * of the given space X ? 2 Problem . When does a sequence { x } in X have the property that the lim x * x , exists for each a * in X * ? 3 Problem . When does a ...
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 ( tu ) 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 ( tu ) T ( t ) T ( u ) , T ( 0 ) = 1 , t , u ≥ 0 . An operator valued function T ( t ) ...
Page 777
... problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9-12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . 14. Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ...
... problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9-12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . 14. Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ...
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