Linear Operators, Part 2 |
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Page 2194
... algebra of all operators of the form ƒ ƒ ( \ ) 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 ( \ ) 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero