Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 67
Page 2094
... subspace YX and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
... subspace YX and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
Page 2113
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
Page 2114
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if o is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
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