Linear Operators: Spectral operators |
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Page 2285
... denoted by the single letter h . We shall define a map A of X into H. Let D ( A ) = { x | E „ x = D ( Aŋ ) for all n and Define Ex ... denote the range of the resolution of the identity E ( ) of Q and XVIII.3.35 2285 MULTIPLICITY THEORY.
... denoted by the single letter h . We shall define a map A of X into H. Let D ( A ) = { x | E „ x = D ( Aŋ ) for all n and Define Ex ... denote the range of the resolution of the identity E ( ) of Q and XVIII.3.35 2285 MULTIPLICITY THEORY.
Page 2436
... denotes the restriction of S to the subspace Co ( E " ) of D ( S ) , then So WT , W - 1 S. Se Let v denote the measure on E " defined by v ( e ) = √ . ( 1 + | x | * ) dx , so that by Theorem III.10.4 we have ( 13 ) ___ 90 ( x ) v ( dx ) ...
... denotes the restriction of S to the subspace Co ( E " ) of D ( S ) , then So WT , W - 1 S. Se Let v denote the measure on E " defined by v ( e ) = √ . ( 1 + | x | * ) dx , so that by Theorem III.10.4 we have ( 13 ) ___ 90 ( x ) v ( dx ) ...
Page 2466
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e1 ) = 0 . Put μ = v + λ . Let H ' denote the set of all sequences ƒ ...
... denote the real axis , the Lebesgue measure on R , and v a finite positive λ - singular measure on R , so that there exists a A - null set e , such that v ( R − e1 ) = 0 . Put μ = v + λ . Let H ' denote the set of all sequences ƒ ...
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