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 2149
... condition ( B ) , are auto- matically satisfied . Thus , for the special types of operators , condition ( B ) becomes the condition which is necessary as well as sufficient for the oper- ator to be a spectral operator . 1 LEMMA . Condition ...
... condition ( B ) , are auto- matically satisfied . Thus , for the special types of operators , condition ( B ) becomes the condition which is necessary as well as sufficient for the oper- ator to be a spectral operator . 1 LEMMA . Condition ...
Page 2153
... condition ( D ) more carefully and see that conditions ( B ) and ( G ) come very near to implying condition ( D ) . This will allow us to replace condition ( D ) , and in a variety of ways , by more satisfactory conditions . For example ...
... condition ( D ) more carefully and see that conditions ( B ) and ( G ) come very near to implying condition ( D ) . This will allow us to replace condition ( D ) , and in a variety of ways , by more satisfactory conditions . For example ...
Page 2162
... condition ( G ) will be a spectral operator of type m - 1 if and only if the constant function v ( § ) = m is an index function . For convenience of reference this finite rate of growth condition is stated formally as follows . 17 ...
... condition ( G ) will be a spectral operator of type m - 1 if and only if the constant function v ( § ) = m is an index function . For convenience of reference this finite rate of growth condition is stated formally as follows . 17 ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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