Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
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).
$∑_{k=0}^{m} (-1)^{k} ({m \atop k}) ||T^{k}x||^{p} = 0$.
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).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
249-255
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
autor
- Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
autor
- Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-4