Linear Operators: Spectral operators |
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Page 2214
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
Page 2217
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. 1 PROOF . Let ...
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. 1 PROOF . Let ...
Page 2218
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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Common terms and phrases
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