Linear Operators: Spectral operators |
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Page 2214
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. 1 PROOF . It was observed in the ...
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. 1 PROOF . It was observed in the ...
Page 2217
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. 1 PROOF . Let ...
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. 1 PROOF . Let ...
Page 2218
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
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