MATHEMATICA BOHEMICA, Vol. 125, No. 1, pp. 87-97 (2000)

$n$-inner product spaces and projections

Aleksander Misiak, Alicja Ryz

Aleksander Misiak, Alicja Ryz, Instytut Matematyki, Politechnika Szczecinska, Al. Piastow 17, 70-310 Szczecin, Poland

Abstract: This paper is a continuation of investigations of $n$-inner product spaces given in \cite {five,six,seven} and an extension of results given in \cite {three} to arbitrary natural $n$. It concerns families of projections of a given linear space $L$ onto its $n$-dimensional subspaces and shows that between these families and $n$-inner products there exist interesting close relations.

Keywords: $n$-inner product space, $n$-normed space, $n$-norm of projection

Classification (MSC2000): 46C05, 46C50

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