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