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Some geometric properties of a sequence space related to ℓp

Published online by Cambridge University Press:  17 April 2009

Mursaleen
Mursaleen
Affiliation:
Department of Mathematics, A.M.U. Aligarh-202002, India e-mail: [email protected]
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Abstract

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The sequence space m (ø), introduced and studied by W.L.C. Sargent in 1960, is closely related to the space ℓp. In this paper we obtain an explicit formula for the Hausdorff measure of noncompactness of any bounded subset in m (ø). We also show that m (ø)enjoys the weak Banach-Saks property, while C (m (ø)) = 2. This shows that the condition C (X) < 2, known to be sufficient for the space X to have the weak Banach-Saks property, is not a necessary one.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 343 - 347
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Ayerbe, J.M. and Benavides, T.D., ‘Connections between some Banach space coefficients concerning normal structure’, J. Math. Anal. Appl. 172 (1993), 53–61.CrossRefGoogle Scholar
[2]Banás, J. and Goebel, K., Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Appl. Math. 60 (Marcel Dekker, New York, Basel, 1980).Google Scholar
[3]Cui, Y. and Hudzik, H., ‘On the Banach-Saks and weak Banach-Saks properties of some Banach sequence spaces’, Acta Sci. Math. (Szeged) 65 (1999), 179–187.Google Scholar
[4]Diestel, J., Sequence and series in Banach spaces, Graduate Texts in Math. 92 (Springer-Verlag, Berlin, Heidelberg, New York, 1984).CrossRefGoogle Scholar
[5]Goldenstein, L.S., Gohberg, I.T. and Markus, A.S., ‘Investigation of some properties of bounded linear operators in connection with their q-norms’, Učem. Zap. Kishinevsk. Un-ta 29 (1957), 29–36.Google Scholar
[6]Malkowsky, E. and Mursaleen, , ‘Matrix transformations between FK-spaces and the sequence sapces m (ø) and n (ø)’, J. Math. Anal. Appl. 196 (1995), 659–665.CrossRefGoogle Scholar
[7]Sargent, W.L.C., ‘Some sequence spaces related to the ℓp spaces’, J. London Math. Soc. 35 (1960), 161–171.CrossRefGoogle Scholar