Linear Operators: Spectral operators |
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Page 2460
... operators . 9 THEOREM . Let H be a self adjoint operator in H , with domain D ( H ) and resolution of the identity E ( · ) . Let V be a symmetric operator in H , with domain D ( V ) . Suppose that D ( V ) ≥ D ( H ) , that the operator ...
... operators . 9 THEOREM . Let H be a self adjoint operator in H , with domain D ( H ) and resolution of the identity E ( · ) . Let V be a symmetric operator in H , with domain D ( V ) . Suppose that D ( V ) ≥ D ( H ) , that the operator ...
Page 2466
... operator F ( H ) is given by ( 39 ) F ( H ) = 9 , where g ( a ) = F ( a ) f ( a ) . 1 Leto denote the set of all symmetric operators V in 5 ' such that the operator V ( iI — H ) -1 is compact , and such that the operator ( ¿ I — H ) ...
... operator F ( H ) is given by ( 39 ) F ( H ) = 9 , where g ( a ) = F ( a ) f ( a ) . 1 Leto denote the set of all symmetric operators V in 5 ' such that the operator V ( iI — H ) -1 is compact , and such that the operator ( ¿ I — H ) ...
Page 2478
... operator in H1 with domain D ( H4 ) and resolution of the identity E4 ( ) . Suppose that V4 is a symmetric operator in H , that D ( V4 ) ≥ D ( H4 ) , that the operator V4 ( iI – H1 ) ̄1 is compact , and that for each bounded interval e ...
... operator in H1 with domain D ( H4 ) and resolution of the identity E4 ( ) . Suppose that V4 is a symmetric operator in H , that D ( V4 ) ≥ D ( H4 ) , that the operator V4 ( iI – H1 ) ̄1 is compact , and that for each bounded interval e ...
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