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On semi inner product spaces over quaternions

Published online by Cambridge University Press:  09 April 2009

Dilip Kumar Sen
Dilip Kumar Sen
Affiliation:
Department of Pure Mathematics University of Calcutta35, Ballygunge Circular Road Calcutta - 700019, India
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Abstract

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In this note semi inner product spaces over quaternions are studied. We investigate the properties of complex strict convexity over C, left and right Q-complex strict convexity over Q, and left and right quaternion strict convexity. Finally we discuss the permanence properties with respect to formation of products.

Keywords

left and right semi inner productsQ-complexQ-strict convexity.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 190 - 204
Copyright
Copyright © Australian Mathematical Society 1984

References

Beesack, P. R., Hughes, E. and Ortel, M. (1979), ‘Rotund complex normed linear spaces’, Proc. Amer. Math. Soc. 75, 42–44.CrossRefGoogle Scholar
Giles, J. R. (1967), ‘Classes of semi inner product spaces’, Trans. Amer. Math. Soc. 129, 436–446.CrossRefGoogle Scholar
Gudder, S. and Strawther, D. (1976), ‘Strictly convex normed linear spaces’, Proc. Amer. Math. Soc. 59, 263–267.CrossRefGoogle Scholar
Holub, J. R. (1975), ‘Rotundity, orthogonality and characterizations of inner product spaces’, Bull. Amer. Math. Soc. 81 (6), 1087–1089.CrossRefGoogle Scholar
Istratescu, V. I. (1979a), ‘On complex strictly convex spaces-I’, J. Math. Anal. Appl. 70, 423–429.CrossRefGoogle Scholar
Istratescu, V. I. (1979b), ‘On complex strictly convex spaces-II’, J. Math. Anal. Appl. 71, 580–589.CrossRefGoogle Scholar
Jamison, J. E. (1982), ‘Banach spaces with the strong maximum modulus property’, Abstracts Amer. Math. Soc. 3, 355.Google Scholar
Köethe, G. (1969), Topological vector spaces, Volume I (Springer-Verlag, Berlin).Google Scholar
Lumer, G. (1961), ‘Semi inner product spaces’, Trans. Amer. Math. Soc. 100, 29–43.CrossRefGoogle Scholar
Sen, D. K. (1981), ‘Characterization of strict convexity’, Bull. Calcutta Math. Soc. 73, 93–97.Google Scholar
Torgashev, A. (1974), ‘A generalisation of inner and semi inner product spaces’, Math. Vesnik, 11 (26), 301–311.Google Scholar
Torgashev, A. (1976), ‘On the numerical range of an operator in a normed space’, Math. Vesnik. 13 (28), 118–124.Google Scholar
Torrance, F. (1970), ‘Strictly convex spaces via semi inner product space orthogonality’, Proc. Amer. Math. Soc. 26, 108–110.CrossRefGoogle Scholar
Throp, E. and Whitley, R. (1967), ‘The strong maximum modulus theorem for analytic functions into a Banach space’, Proc. Amer. Math. Soc. 18, 640–646.CrossRefGoogle Scholar