Linear Operators: Spectral operators |
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Page 1936
... restriction TE , X is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( o ; T ) in the resolution of the identity for T ...
... restriction TE , X is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( o ; T ) in the resolution of the identity for T ...
Page 2094
... restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace Y ...
... restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace Y ...
Page 2228
... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , TE ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , TE ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operators Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero