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arXiv · 1308.0974

Semi-inner products and the concept of semi-polarity

Ákos G. Horváth·Zsolt Lángi·Margarita Spirova
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Abstract

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

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Ákos G. Horváth, Zsolt Lángi, Margarita Spirova. 2013-08-05. Semi-inner products and the concept of semi-polarity. https://doi.org/10.1007/s00025-015-0510-y

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