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Page 479
... adjoint T ** : X ** → ** is an extension of T. If X is reflexive then T ** T. PROOF . Let xe X , y * € Y * . Then , Q.E.D. 7 ( T ** ) y * = T * y * = ( T * y * ) = y * Tử = ( Tâ ) y * ( Îî ) y * . LEMMA . A linear operator T in B ( X ...
... adjoint T ** : X ** → ** is an extension of T. If X is reflexive then T ** T. PROOF . Let xe X , y * € Y * . Then , Q.E.D. 7 ( T ** ) y * = T * y * = ( T * y * ) = y * Tử = ( Tâ ) y * ( Îî ) y * . LEMMA . A linear operator T in B ( X ...
Page 538
... adjoint operator goes back to matrix theory and to the theories of differential and integral equations . In the spaces L , p 1 , and la , Riesz [ 2 ; p . 478 , 6 ; p . 85 ] made use of this notion and proved the validity of Lemma 2.2 ...
... adjoint operator goes back to matrix theory and to the theories of differential and integral equations . In the spaces L , p 1 , and la , Riesz [ 2 ; p . 478 , 6 ; p . 85 ] made use of this notion and proved the validity of Lemma 2.2 ...
Page 794
... operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian ... adjoint differential operators of the second order . Doklady Akad . Nauk ... adjoint differential operators of the second order . Uspehi Matem . Nauk ( N. S. ) 8 ...
... operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian ... adjoint differential operators of the second order . Doklady Akad . Nauk ... adjoint differential operators of the second order . Uspehi Matem . Nauk ( N. S. ) 8 ...
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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ