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A commutativity criterion for prespectral operators

Published online by Cambridge University Press:  17 April 2009

Werner Ricker
Werner Ricker
Affiliation:
Centre for Mathematical Analysis, Australian National University, Canberra, Australian Capital Territory, 2600Australia.
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Abstract

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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 (·).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 113 - 119
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Dowson, H.R., Spectral theory of linear operators, London Math. Soc. Monograph No. 12 (Academic Press, London, 1978).Google Scholar
[2]Nagy, B., On Boolean algebras of projections and prespectral operators, Operator Theory: Advances and Applications Vol. 6 (Birkhauser Verlag, Basel, 1982) 145–162.Google Scholar