Linear Operators: Spectral operators |
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Page 2147
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( S ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( S ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
Page 2162
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ 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 operator 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 subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero