Linear Operators: Spectral operators |
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Page 1926
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations T N = 1- Σ λε ( λ ) , E ...
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined by the equations T N = 1- Σ λε ( λ ) , E ...
Page 1941
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
Page 1963
... arbitrary , shows that by ay . Since B ( 5 " ) is a B * -algebra ( IX.3.2 ) under the involution . A → A * , it follows that the map ( a1 ; ) → ( b1 , ) is an involution in the algebra M , ( B ( S ) ) and that , with this involution ...
... arbitrary , shows that by ay . Since B ( 5 " ) is a B * -algebra ( IX.3.2 ) under the involution . A → A * , it follows that the map ( a1 ; ) → ( b1 , ) is an involution in the algebra M , ( B ( S ) ) and that , with this involution ...
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