Linear Operators: Spectral operators |
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Page 1930
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
Page 2043
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( S ) > 0 so that = | S | et with —π / 2 < 0 < π / 2 . Then since ...
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( S ) > 0 so that = | S | et with —π / 2 < 0 < π / 2 . Then since ...
Page 2087
... plane R ( ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into 5 " which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , q ...
... plane R ( ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into 5 " which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , q ...
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