Linear Operators: Spectral operators |
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Page 2118
... operator T defined by ( Tf ) ( t ) = tf ( t ) , t € [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for 9 € C ° . It is proved ( see Foias [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
... operator T defined by ( Tf ) ( t ) = tf ( t ) , t € [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for 9 € C ° . It is proved ( see Foias [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
Page 2120
... spectral function if ( i ) the map f → U , is an alge- braic homomorphism with UI , and ( ii ) the map → U12 of Q into B ( X ) is analytic on the complement of the support of f ... operator and N is a 2120 XV.16 XV . SPECTRAL OPERATORS.
... spectral function if ( i ) the map f → U , is an alge- braic homomorphism with UI , and ( ii ) the map → U12 of Q into B ( X ) is analytic on the complement of the support of f ... operator and N is a 2120 XV.16 XV . SPECTRAL OPERATORS.
Page 2590
... operator , definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a ...
... operator , definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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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