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

Shiv Lal | Zendy; Siladitya Bhattacharya | Zendy; C. Sreedhar | Zendy

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

Author(s) -

Shiv Lal,

Siladitya Bhattacharya,

C. Sreedhar

Publication year - 2001

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1003

Subject(s) - extension (predicate logic) , mathematics , continuous linear operator , pure mathematics , linear extension , discrete mathematics , computer science , partially ordered set , programming language

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.

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