Linear Operators: Spectral operators |
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Page 2098
... result for spectral measures due to Lorch [ 1 ] and Mackey [ 4 ] . The proof given here depends on the result , due to Sz . - Nagy [ 7 ] , that a bounded Abelian group of operators in a Hilbert space is equivalent to a unitary group ...
... result for spectral measures due to Lorch [ 1 ] and Mackey [ 4 ] . The proof given here depends on the result , due to Sz . - Nagy [ 7 ] , that a bounded Abelian group of operators in a Hilbert space is equivalent to a unitary group ...
Page 2214
... result of Bade , which was described in the introduc- tion . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it ...
... result of Bade , which was described in the introduc- tion . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it ...
Page 2291
... result gives conditions under which such an operator , if spectral , remains spectral after a perturbation . The results are directed toward the applications to nonselfadjoint differential operators which follow in the next two sections ...
... result gives conditions under which such an operator , if spectral , remains spectral after a perturbation . The results are directed toward the applications to nonselfadjoint differential operators which follow in the next two sections ...
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