Linear Operators: Spectral operators |
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Page 2194
... algebra of all operators of the form ƒ ƒ ( λ ) E ( dλ ) where ƒ is E ... projections in its resolution of the identity , the problem of the present ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
... algebra of all operators of the form ƒ ƒ ( λ ) E ( dλ ) where ƒ is E ... projections in its resolution of the identity , the problem of the present ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
Page 2217
... algebra of projections in a B - space X , and let B1 be its strong closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone ...
... algebra of projections in a B - space X , and let B1 be its strong closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone ...
Page 2218
... algebra generated by B1 . Every operator in such a uniformly closed algebra is , by Lemma 9 , given in terms of a ... projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
... algebra generated by B1 . Every operator in such a uniformly closed algebra is , by Lemma 9 , given in terms of a ... projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
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