Linear Operators: Spectral operators |
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Page 1951
... linear subspace of X , then the set of bounded linear operators A in X for which AX is a closed right ideal in B ( x ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ( o ) ...
... linear subspace of X , then the set of bounded linear operators A in X for which AX is a closed right ideal in B ( x ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ( o ) ...
Page 2214
... linear combinations of elements of B. It follows that A leaves invariant every closed linear manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ...
... linear combinations of elements of B. It follows that A leaves invariant every closed linear manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
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