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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 1, 2001, pp. 35–53
DOI: 10.4171/ZAA/1003

Published online: 2001-03-31

Complex 2-Normed Linear Spaces and Extension of Linear 2-Functionals

S.N. Lal[1], S. Bhattacharya[2] and C. Sreedhar[3]

(1) Banaras Hindu University, Varanasi, India
(2) Banaras Hindu University, Varanasi, India
(3) Banaras Hindu University, Varanasi, India

The known concept of 2-normed real linear spaces is extended to 2-normed complex linear spaces. This extension is not trivial. A Hahn-Banach type extension theorem for complex linear 2-functionals is established and it is shown that it is not possible to get this result from the known Hahn-Banach type extension theorem for real linear 2-functionals using the Bohnenblust-Sobczyk technique directly as is done in the case of linear functionals. As an application of our extension theorem, a 2-norm version of the Ascoli-Mazur theorem on tangent functionals is established. Several examples and counter examples illustrate the results obtained in the paper.

Keywords: 2-norms, linear, convex, 2-bounded and tangent 2-functionals, internal and bounding points

Lal S.N., Bhattacharya S., Sreedhar C.: Complex 2-Normed Linear Spaces and Extension of Linear 2-Functionals. Z. Anal. Anwend. 20 (2001), 35-53. doi: 10.4171/ZAA/1003