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 ( t + u ) T ( t ) T ( u ) , T ( 0 ) = I , 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 ) = I , 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 ) . Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) ...
... problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9-12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . Solution of the inverse Sturm - Liouville problem . Doklady Akad . Nauk SSSR ( N. S. ) ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian 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