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 * in X * ? n 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 * in X * ? n 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 ) = 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 ) ...
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
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ