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Page 479
... adjoint T ** : X ** → Y ** is an extension of T. If X is reflexive then T ** = T. PROOF . Let xe X , y * € Y * . Then , Q.E.D. ( T ** x ) 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 ** = T. PROOF . Let xe X , y * € Y * . Then , Q.E.D. ( T ** x ) 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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ