Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 60
Page 2194
... algebra of all operators of the form ƒ ƒ ( λ ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full ... 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 - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
Page 2195
... Boolean algebra B of projections in a B - space X is said to be complete ( o - complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a greatest lower bound and a least upper bound in B. The Boolean algebra B is ...
... Boolean algebra B of projections in a B - space X is said to be complete ( o - complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a greatest lower bound and a least upper bound in B. The Boolean algebra B is ...
Page 2217
... Boolean 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 ...
... Boolean 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 ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
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