Linear Operators: Spectral operators |
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Page 2094
... invariant closed subspace Y 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 is given by E. Moreover , Dowson [ 1 ] proved that o ( T | ) ≤ σ ...
... invariant closed subspace Y 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 is 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 . To ...
... 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 . To ...
Page 2286
... invariant under B and those of H invariant under B , the resolution of the identity of Q. 37 DEFINITION . If M is a closed invariant subspace in X , we denote by D ( M ) the closure in H of the linear set A ( M ◇ D ( A ) ) . Similarly ...
... invariant under B and those of H invariant under B , the resolution of the identity of Q. 37 DEFINITION . If M is a closed invariant subspace in X , we denote by D ( M ) the closure in H of the linear set A ( M ◇ D ( A ) ) . Similarly ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero