Linear Operators: Spectral operators |
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Page 1930
... countably additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel ...
... countably additive . However , in Corollary X.2.4 we have seen that a bounded normal operator in Hilbert space always has a uniquely defined bounded and countably additive . resolution of the identity defined on the field of all Borel ...
Page 1931
... countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the ...
... countably additive spectral measure E is a o - field , then E is countably additive in the strong operator topology and bounded . The boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral operators in the ...
Page 2144
... countably additive in the X topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed o the family of d for which the equation is valid is a σ ...
... countably additive in the X topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed o the family of d for which the equation is valid is a σ ...
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