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\(n\)-inner product spaces and projections. (English) Zbl 0970.46013

Summary: This paper is a continuation of investigations of \(n\)-inner product spaces given in A. Misiak [Math. Nachr. 140, 299-319 (1989; Zbl 0673.46012); ibid. 143, 249-261 (1989; Zbl 0708.46025); Pr. Nauk. Politech. Szczec. 411, Inst. Mat. 12, 63-74 (1991; Zbl 0754.15027)] and an extension of results given in S. Gähler, Z. Zekanowski [Demonstr. Math. 19, 747-766 (1986; Zbl 0627.46022)] 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.

MSC:

46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
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