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 2095
... operator T is spectral if and only if the restriction TV is spectral . Consequently , the analogs of the results stated in the preceding paragraph for restrictions of spectral and scalar type operators also hold for their quotients ...
... operator T is spectral if and only if the restriction TV is spectral . Consequently , the analogs of the results stated in the preceding paragraph for restrictions of spectral and scalar type operators also hold for their quotients ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator . Moreover , if A is adjoint Abelian and is weakly complete , then A is scalar type if and only if either ( a ) A is invertible ...
Page 2174
... operator - valued function defined on rectangles . In a Hilbert space the condition that lettr | ≤ M for all t e R implies that T is equivalent to a self adjoint operator and hence is a scalar type operator with real spectrum . ( This ...
... operator - valued function defined on rectangles . In a Hilbert space the condition that lettr | ≤ M for all t e R implies that T is equivalent to a self adjoint operator and hence is a scalar type operator with real spectrum . ( This ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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