Linear Operators: Spectral operators |
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Page 1938
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Page 2111
... operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes outside o ( T ) . Moreover , T is a scalar type spectral operator if and only if every vector has a ...
... operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes outside o ( T ) . Moreover , T is a scalar type spectral operator if and only if every vector has a ...
Page 2242
... spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the ...
... spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the ...
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