Semi-inner products and the concept of semi-polarity

G. Horváth, Ákos and Lángi, Zsolt and Spirova, Margarita (2015) Semi-inner products and the concept of semi-polarity. Results in Mathematics. ISSN 1422-6383 (print version), 1420-9012 (electronic version) (Submitted)

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Abstract

The lack of an inner product structure in general Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for symmetry, than the one determing a Hilbert space. We use the semi-inner product on a finite dimensional real Banach space to define and investigate three concepts. First, we generalize that of antinorms, already defined in Minkowski planes, for even dimensional spaces. Second, we introduce normality maps, which leads us, in the third part, to the study of semi-polarity, a variant of the notion of polarity which makes use of the underlying semi-inner product.

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