Linear Operators: Spectral operators |
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Page 2144
... topology of X * , and is bounded . It remains only to show that A ( o ) A ... operator in the weakly complete complex B - space X and let E be the associated ... strong operator topology . This extension is bounded and commutes with T ...
... topology of X * , and is bounded . It remains only to show that A ( o ) A ... operator in the weakly complete complex B - space X and let E be the associated ... strong operator topology . This extension is bounded and commutes with T ...
Page 2194
... strong operator topology . Thus the strong and weak operator closures of an algebra of operators are the same . This section , like the last one , starts with a commuting family of spectral operators together with their resolutions of ...
... strong operator topology . Thus the strong and weak operator closures of an algebra of operators are the same . This section , like the last one , starts with a commuting family of spectral operators together with their resolutions of ...
Page 2204
... strong operator topology . Thus x * E x = xA ( e ) x * , which proves that ∞ e is in and shows that Σ consists of all Borel sets in 4. This means that for every Borel set e in 4 there is a projection E ( e ) in B with A ( e ) = E ( e ) ...
... strong operator topology . Thus x * E x = xA ( e ) x * , which proves that ∞ e is in and shows that Σ consists of all Borel sets in 4. This means that for every Borel set e in 4 there is a projection E ( e ) in B with A ( e ) = E ( e ) ...
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