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On convergence in \(n\)-inner product spaces. (English) Zbl 1185.15022

Summary: We discuss the notions of strong convergence and weak convergence in \(n\)-inner product spaces and study the relation between them. In particular, we show that the strong convergence implies the weak convergence and disprove the converse through a counter-example, by invoking an analogue of Parseval’s identity in \(n\)-inner product spaces.

MSC:

15A63 Quadratic and bilinear forms, inner products
46C99 Inner product spaces and their generalizations, Hilbert spaces
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