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On \(A\)-linear operators on a Hilbert \(A\)-module. (English) Zbl 0953.46025

Summary: The aim of this note is to prove that on every Hilbert \(A\)-module \(H\) over a proper \(\text{H}^*\)-algebra \(A\), the \(p\)-norms of Smith \((1\leq p\leq\infty)\) induce the same bounded \(A\)-operators with the same bounds.

MSC:

46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46C99 Inner product spaces and their generalizations, Hilbert spaces
46K15 Hilbert algebras
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