Linear Operators: General theory |
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Page 479
... adjoint T ** : X ** → Y ** is an extension of T. If X is reflexive then T ** PROOF . Let xe X , y * € Y * . Then , Q.E.D. - T. ( T ** â ) y * = & T * y * = ( T * y * ) x = y * Tx = ( Îâ ) y * . 7 LEMMA . A linear operator T in B ( X ...
... adjoint T ** : X ** → Y ** is an extension of T. If X is reflexive then T ** PROOF . Let xe X , y * € Y * . Then , Q.E.D. - T. ( T ** â ) y * = & T * y * = ( T * y * ) x = y * Tx = ( Îâ ) y * . 7 LEMMA . A linear operator T in B ( X ...
Page 612
... adjoint operator ( which may have void point spectrum ) on a separable Hilbert space , then a self adjoint compact operator K may be found such that T ÷ K has enough eigenvectors to span the entire space . This result was extended to ...
... adjoint operator ( which may have void point spectrum ) on a separable Hilbert space , then a self adjoint compact operator K may be found such that T ÷ K has enough eigenvectors to span the entire space . This result was extended to ...
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 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