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A note on strong Markuševič of decompositions of Banach spaces

Published online by Cambridge University Press:  17 April 2009

P.K. Jain  and
D.P. Sinha
P.K. Jain
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110007, India
D.P. Sinha
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110007, India
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Abstract

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The space l∞ is known to have no Schauder decomposition. It is proved here that l∞ does not even possess any strong Markuševič decomposition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 239 - 244
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bachelis, G.F. and Rosenthal, H.P., ‘On unconditionally converging series and biorthogonal systems in Banach spaces’, Pacific J. Math. 37 (1971), 1–5.CrossRefGoogle Scholar
[2]Dean, D.W., ‘Schauder decompositions in (m)’, Proc. Amer. Math. Soc. 18 (1967), 619–623.Google Scholar
[3]Diestel, J., Geometry of Banach spaces - selected topics: Lecture notes in Math. 485 (Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[4]Dunford, N. and Schwartz, J.T., Linear operators I, General Theory (Interscience, 1958).Google Scholar
[5]Jain, P.K. and Sinha, D.P., ‘On Markuševič decompositions of Banach spaces’, Anal. Math. 16 (1990), 265–275.CrossRefGoogle Scholar
[6]Jain, P.K. and Sinha, D.P., ‘On strong Markusevic decompositions of Banach spaces’, J. Indian Math. Soc. 55 (1990), 117–126.Google Scholar
[7]Lindenstrauss, J., ‘Weakly compact sets — their topological properties and the Banach spaces they generate’, Proc. Sympos, on ‘Infinite dimensional topology’ held in Baton-Rouge, Ann. of Math. Studies 69 (1972), 235–274.Google Scholar
[8]Rainwater, J., ‘Local uniform convexity of Day's norm on c0(Γ)’, Proc. Amer. Math. Soc. 22 (1969), 335–339.Google Scholar
[9]Sanders, B.L., ‘On the existence of Schauder decompositions in Banach spaces’, Proc. Amer. Math. Soc. 16 (1965), 987–990.CrossRefGoogle Scholar
[10]Singer, I., Bases in Banach spaces II (Springer-Verlag, Berlin, Heidelberg, New York, 1981).CrossRefGoogle Scholar
[11]Troyanski, S., ‘On locally uniformly convex and differentiable norms in certain non-separable Banach spaces’, Studia Math. 37 (1971), 173–180.CrossRefGoogle Scholar