Linear Operators: Spectral operators |
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Page 1936
... identity for the 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 ...
... identity for the 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 ...
Page 2094
... identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where ** , then it has a unique resolution of the identity of class ( T ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique ...
... identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where ** , then it has a unique resolution of the identity of class ( T ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has a unique ...
Page 2242
... identity for T in the sense of Definition 12 is the same as the resolution of the identity for T in the sense of Definition 1 . PROOF . Using the notations of Definitions 12 and 1 , let T and E have all the properties of Definition 12 ...
... identity for T in the sense of Definition 12 is the same as the resolution of the identity for T in the sense of Definition 1 . PROOF . Using the notations of Definitions 12 and 1 , let T and E have all the properties of Definition 12 ...
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