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 invariant ; in this case the resolution of the identity of Tis given by E. Moreover , Dowson [ 1 ] proved that o ( T | ) ≤ σ ...
... invariant closed subspace of X is spectral if and only if the resolution of the identity E of T also leaves invariant ; in this case the resolution of the identity of Tis given by E. Moreover , Dowson [ 1 ] proved that o ( T | ) ≤ σ ...
Page 2214
... invariant every closed linear manifold which is invariant under every member of B. 1 PROOF . It was observed in the preceding proof that an operator in the weakly closed algebra generated by B has the required invariance property . Το ...
... invariant every closed linear manifold which is invariant under every member of B. 1 PROOF . It was observed in the preceding proof that an operator in the weakly closed algebra generated by B has the required invariance property . Το ...
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 So , ( 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 So , ( E ( e ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero