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A direct proof of a theorem of West on sequences of Riesz operators

Published online by Cambridge University Press:  18 May 2009

Anthony F. Ruston
Affiliation:
University College of North Wales, (Coleg Prifysgol Gogledd Cymru), Bangor, Caernarvonshire, LL57 2Uw, Wales
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We recall (cf. [2] Definitions 3.1 and 3.2, p. 322) that a bounded linear operator T on a Banach space ℵ into itself is said to be asymptotically quasi-compact if K(Tn)n → 0 as n → ∞. where K(U) = inf ∥U–C∥ for every bounded linear operator U on ℵ into itself, the infimum being taken over all compact linear operators C on ℵ into itself. For a complex Banach space, this is equivalent (cf. [2], pp. 319, 321 and 326) to T being a Riesz operator.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

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4.West, T. T., The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737752.CrossRefGoogle Scholar