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Page 479
... adjoint T ** : X ** →→ ) ** is an extension of T. If X is reflexive then T ** 6 PROOF . Let xe X , y * € Y * . Then , ( T *** ) y * = T * y * = ( T * y * ) x = y * Tx = ( Îâ ) y * . Q.E.D. 7 LEMMA . A linear operator T in B ( X , Y ) ...
... adjoint T ** : X ** →→ ) ** is an extension of T. If X is reflexive then T ** 6 PROOF . Let xe X , y * € Y * . Then , ( T *** ) y * = T * y * = ( T * y * ) x = y * Tx = ( Îâ ) y * . Q.E.D. 7 LEMMA . A linear operator T in B ( X , Y ) ...
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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ