Linear Operators: Spectral operators |
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Page 1922
... Commutative B - Algebras of Spectral Operators 2179 3. Strongly Closed Algebras and Complete Boolean Algebras 2194 4. Strong Limits of Spectral Operators : 5 . Non - Commutative Case Exercises 6. Notes and Remarks 2219 2222 2225 XVIII ...
... Commutative B - Algebras of Spectral Operators 2179 3. Strongly Closed Algebras and Complete Boolean Algebras 2194 4. Strong Limits of Spectral Operators : 5 . Non - Commutative Case Exercises 6. Notes and Remarks 2219 2222 2225 XVIII ...
Page 1964
... commutative B * -algebra with unit ê ( s ) 1 for all s in S. = The symbol will be used for a B * -subalgebra of eB ( S , E ) with the same unit ê . The integral ( 15 ) α = = √_â ( s ) e ( ds ) , â € Â , maps the algebra A into a ...
... commutative B * -algebra with unit ê ( s ) 1 for all s in S. = The symbol will be used for a B * -subalgebra of eB ( S , E ) with the same unit ê . The integral ( 15 ) α = = √_â ( s ) e ( ds ) , â € Â , maps the algebra A into a ...
Page 2179
... commutative algebras of spectral operators which are closed in the uniform operator topology . It will first be shown that such algebras A may be ... COMMUTATIVE B - ALGEBRAS The Structure of Commutative B-Algebras Spectral Operators.
... commutative algebras of spectral operators which are closed in the uniform operator topology . It will first be shown that such algebras A may be ... COMMUTATIVE B - ALGEBRAS The Structure of Commutative B-Algebras Spectral Operators.
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