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A commutativity criterion for prespectral operators
Published online by Cambridge University Press: 17 April 2009
Abstract
It is shown that if a bounded linear operator A commutes with a prespectral operator T of class Γ, then A commutes with the resolution of the identity of class Γ for T, say P (·), if and only if A*(Γ) ⊆ [PC*Γ. Here A* is the dual operator of A and [Pc]*Γ is the linear span of the set {U*ξ U ε P (·) c, ξ ε Γ} where P (·) c denotes the commutant of the range of P (·).
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- Copyright © Australian Mathematical Society 1987
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