Linear Operators: Spectral operators |
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Page 1956
... THEOREM . If T is of finite type , its residual spectrum is void and a point is in its point spectrum if and only if ... follows from Theorem 2 that is in the point spectrum of T. If E ( { } ) = 0 then it follows from Theorem 2 that XI ...
... THEOREM . If T is of finite type , its residual spectrum is void and a point is in its point spectrum if and only if ... follows from Theorem 2 that is in the point spectrum of T. If E ( { } ) = 0 then it follows from Theorem 2 that XI ...
Page 2194
Nelson Dunford, Jacob T. Schwartz. 1 PROOF . The first statement follows from Theorem 3. Let A1 be the algebra of all operators of the form Sƒ ( A ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that ...
Nelson Dunford, Jacob T. Schwartz. 1 PROOF . The first statement follows from Theorem 3. Let A1 be the algebra of all operators of the form Sƒ ( A ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that ...
Page 2243
... follows from Theorem XV.5.1 that ƒ ( T | E ( en ) X ) = Sen ƒ ( \ ) F ( dλ ) , so that = f ( T | E ( en ) X ) E ( en ) x = | ƒ ( ^ ) E ( dλ ) x , S It follows by Theorem 11 that en f ( TE ( en ) X ) E ( en ) x = ƒ2 ( T ) E ( en ) x . x ...
... follows from Theorem XV.5.1 that ƒ ( T | E ( en ) X ) = Sen ƒ ( \ ) F ( dλ ) , so that = f ( T | E ( en ) X ) E ( en ) x = | ƒ ( ^ ) E ( dλ ) x , S It follows by Theorem 11 that en f ( TE ( en ) X ) E ( en ) x = ƒ2 ( T ) E ( en ) x . x ...
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