Geodesic
A direct proof of a theorem of West on sequences of Riesz operators
Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 93-94

Voir la notice de l'article provenant de la source Cambridge University Press

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)1⁄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. 
Ruston, Anthony F. A direct proof of a theorem of West on sequences of Riesz operators. Glasgow mathematical journal, Tome 15 (1974) no. 2, pp. 93-94. doi: 10.1017/S001708950000224X
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[1] 1.Gillespie, T. A. and West, T. T., A characterisation and two examples of Riesz operators, Glasgow Math. J. 9 (1968), 106–110. Google Scholar | DOI

[2] 2.Ruston, A. F., Operators with a Fredholm theory, J. London Math. Soc. 29 (1954), 318–326. Google Scholar | DOI

[3] 3.West, T. T., Riesz operators in Banach spaces, Proc. London Math. Soc. (3) 16 (1966), 131–140. Google Scholar | DOI

[4] 4.West, T. T., The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737–752. Google Scholar | DOI

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