Powers of m-isometries

• Autorzy: Teresa Bermúdez , Carlos Díaz Mendoza , Antonio Martinón
• Języki publikacji: EN

Abstrakty

EN

A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X,
$∑_{k=0}^{m} (-1)^{k} ({m \atop k}) ||T^{k}x||^{p} = 0$.
We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if $T^{r}$ and $T^{r+1}$ are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if $T^{r}$ is an (m,p)-isometry and $T^{s}$ is an (l,p)-isometry, then $T^{t}$ is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l).

Kategorie tematyczne

• 47B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 3
• Strony: 249-255

Daty

wydano

2012

Twórcy

autor

Teresa Bermúdez

• Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain

autor

Carlos Díaz Mendoza

• Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain

autor

Antonio Martinón

• Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain

Identyfikatory

DOI

10.4064/sm208-3-4