Linear Operators: Spectral operators |
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Page 2094
... invariant closed subspace of X is spectral if and only if the resolution of the identity E of T also leaves Y invariant ; in this case the resolution of the identity of T is given by E. Moreover , Dowson [ 1 ] proved that o ( TY ) ≤ σ ...
... invariant closed subspace of X is spectral if and only if the resolution of the identity E of T also leaves Y invariant ; in this case the resolution of the identity of T is given by E. Moreover , Dowson [ 1 ] proved that o ( TY ) ≤ σ ...
Page 2214
... invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding proof that an operator in the weakly closed algebra generated by B has the required invariance property . To ...
... invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding proof that an operator in the weakly closed algebra generated by B has the required invariance property . To ...
Page 2216
... invariant under every element E ( e ) of the resolu- tion of the identity for T. Thus , if P is the orthogonal projection onto Ho then , since E ( e ) leaves H。 invariant , PE ( e ) P = E ( e ) P . If y is orthogonal to Ho , ( E ( e ) ...
... invariant under every element E ( e ) of the resolu- tion of the identity for T. Thus , if P is the orthogonal projection onto Ho then , since E ( e ) leaves H。 invariant , PE ( e ) P = E ( e ) P . If y is orthogonal to Ho , ( E ( e ) ...
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