Linear Operators: Spectral operators |
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Page 2149
... condition ( B ) becomes the condition which is necessary as well as sufficient for the oper- ator to be a spectral operator . 1 LEMMA . Condition ( A ) of Section 2 is satisfied if the spectrum of T is nowhere dense in the complex plane ...
... condition ( B ) becomes the condition which is necessary as well as sufficient for the oper- ator to be a spectral operator . 1 LEMMA . Condition ( A ) of Section 2 is satisfied if the spectrum of T is nowhere dense in the complex plane ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero