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Orthogonality in normed spaces

Published online by Cambridge University Press:  17 April 2009

J. R. Partington
J. R. Partington
Affiliation:
Fitzwilliam College, Cambridge University, England.
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Abstract

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Some properties which different definitions or orthogonality in a normed space can possess are considered. It is shown that orthogonality can be defined on any separable space with many of the properties possessed by the usual orthogonality in an inner-product space, but that the possession of a further property forces the space to be isomorphic to a Euclidean space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 449 - 455
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Day, M. M., Normed linear spaces (Springer-Verlag, Berlin-Heidelberg-New York, 3rd ed., 1973).CrossRefGoogle Scholar
[2]Diestel, J., Geometry of Banach spaces (Springer-Verlag, Berlin-Heidelberg–New York, 1975).CrossRefGoogle Scholar
[3]Diminnie, C. R., “A new orthogonality relation for normed linear spaces”, Math. Nachr. 114 (1983), 197–203.CrossRefGoogle Scholar
[4]Freese, R. W., Diminnie, C. R. and Andalafte, E. Z., “A study of generalized orthogonality relations in normed linear spaces”. Math. Nachr. (to appear).Google Scholar
[5]James, R. C., “Orthogonality in normed linear spaces”, Duke Math. J. 12 (1945), 291–302.CrossRefGoogle Scholar
[6]James, R. C., “Inner products in normed spaces”, Bull. Amer. Math. Soc. 53 (1947), 559–566.CrossRefGoogle Scholar
[7]Lindenstrauss, J. and Tzafriri, L., “On the complemented subspaces problem”, Israel J. Math. 9 (1971), 263–269.CrossRefGoogle Scholar
[8]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I, (Springer-Verlag, Berlin-Heidelberg-New York, 1977).CrossRefGoogle Scholar
[9]Ovsepian, R. I. and Pelczynski, A., “The existence in every separable Banach space of a fundamental total and bounded biorthogonal sequence and related constructions of uniformly bounded orthonormal systems in L 2”, Studia Math. 54 (1975), 149–159.CrossRefGoogle Scholar