Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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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 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 5 of the linear set A ( MD ( A ) ) . Similarly if R ...
... 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 5 of the linear set A ( MD ( A ) ) . Similarly if R ...
Contents
SPECTRAL OPERATORS | 1924 |
The Algebras A and | 1966 |
Some Examples of Bounded Spectral Operators | 1983 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero