Abstract. In this paper we consider the notion of $n$-isometry on a Banach space. We determine the existence of non-isometric $2$-isometries for the classes of weighted shifts and composition operators on $\ell_p$ spaces. We also address similar questions for weighted composition operators acting on the space of scalar valued continuous functions, defined on a compact Hausdorff topological space.
AMS Subject Classification
(1991): 47B33, 47B37
Keyword(s):
$n$-isometries,
weighted composition operators on $l_p$ spaces,
composition operators on ${\cal C}(X)$
Received January 12, 2009, and in revised form July 7, 2009. (Registered under 5/2009.)
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