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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Results 1-3 of 86
Page 2098
... result for spectral measures due to Lorch [ 1 ] and Mackey [ 4 ] . The proof given here depends on the result , due to Sz . - Nagy [ 7 ] , that a bounded Abelian group of operators in a Hilbert space is equivalent to a unitary group ...
... result for spectral measures due to Lorch [ 1 ] and Mackey [ 4 ] . The proof given here depends on the result , due to Sz . - Nagy [ 7 ] , that a bounded Abelian group of operators in a Hilbert space is equivalent to a unitary group ...
Page 2214
... result of Bade , which was described in the introduc- tion . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it ...
... result of Bade , which was described in the introduc- tion . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it ...
Page 2291
... result gives conditions under which such an operator , if spectral , remains spectral after a perturbation . The results are directed toward the applications to nonselfadjoint differential operators which follow in the next two sections ...
... result gives conditions under which such an operator , if spectral , remains spectral after a perturbation . The results are directed toward the applications to nonselfadjoint differential operators which follow in the next two sections ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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Common terms and phrases
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