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

Philipp Hoffmann; Michael Mackey; Mícheál Ó Searcóid

doi:10.1007/s00020-011-1905-0

paper

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

arXiv:1106.0339 · doi:10.1007/s00020-011-1905-0

Abstract

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 $, f or a l l$ x \in X $. I n t hi s p a p er w es t u d y t h es t r u c t u r e w hi c h u n d er l i es t h eseco n d p a r am e t er o f$ (m, p) $- i so m e t r i co p er a t or s . W eco n ce n t r a t eo n d e t er minin g w h e nan$ (m, p) $- i so m e t r y i s a$ (μ, q) $- i so m e t r y f or so m e p ai r ($ μ, q) $. W e a l soe x t e n d t h e d e f ini t i o n o f$ (m, p) $- i so m e t r y, t o in c l u d e$ p=\infty $an d s t u d y ba s i c p r o p er t i eso f t h ese$ (m, \infty)$-isometries.

Cited by in corpus (1)

$(m, p)$ -isometric and $(m, \infty)$ -isometric operator tuples on normed spaces

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

Abstract

Cited by in corpus (1)

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