On the second parameter of an $(m, p)$-isometry

Details On the second parameter of an $(m, p)$-isometry On the second parameter of an $(m, p)$-isometry

2011-06-01

arxiv.org/abs/1106.0339v6

Integr. Equ. Oper. Theory 71 (2011), 389-405

Mathematics

Functional Analysis

Scientific paper

10.1007/s00020-011-1905-0

A bounded linear operator $T$ on a Banach space $X$ is called an $(m, p)$-isometry if it satisfies the equation \sum_{k=0}^{m}(-1)^{k} {m \choose k}\|T^{k}x\|^{p} = 0$, for all $x \in X$. In this paper we study the structure which underlies the second parameter of $(m, p)$-isometric operators. We concentrate on determining when an $(m, p)$-isometry is a $(\mu, q)$-isometry for some pair ($\mu, q)$. We also extend the definition of $(m, p)$-isometry, to include $p=\infty$ and study basic properties of these $(m, \infty)$-isometries.

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