Linear Operators: Spectral operators |
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Page 1936
... restriction T | EX is the corresponding restriction of the resolution of the identity for T. i PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of the identity for ...
... restriction T | EX is the corresponding restriction of the resolution of the identity for T. i PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( σ ; T ) in the resolution of the identity for ...
Page 2094
... restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of X ...
... restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of X ...
Page 2228
... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , T | E ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
... restriction T | E ( o ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , T | E ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
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