Linear Operators: Spectral operators |
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Page 1930
... resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , o ( Ts ) ≤ 8 , δε Σ . δ Here we have used , and shall continue to use , the symbol T , for the restriction TX , of T to the manifold X ...
... resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , o ( Ts ) ≤ 8 , δε Σ . δ Here we have used , and shall continue to use , the symbol T , for the restriction TX , of T to the manifold X ...
Page 2094
... resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where г ≤ X ** , then it has a unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( Ã ) ...
... resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where г ≤ X ** , then it has a unique resolution of the identity of class ( I ) . If X * is weakly complete and T is spectral of class ( Ã ) ...
Page 2242
... 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 sense of Definition 1. Moreover , the resolution of the identity for T in the sense ...
... 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 sense of Definition 1. Moreover , the resolution of the identity for T in the sense ...
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