### Meromorphic functional calculus and local spectral theory.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

The problem we are concerned with in this research announcement is the algebraic characterization of chain-finite operators (global case) and of locally chain-finite operators (local case).

We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

Our aim in this paper is to prove that every separable infinite-dimensional complex Banach space admits a topologically mixing holomorphic uniformly continuous semigroup and to characterize the mixing property for semigroups of operators. A concrete characterization of being topologically mixing for the translation semigroup on weighted spaces of functions is also given. Moreover, we prove that there exists a commutative algebra of operators containing both a chaotic operator and an operator which...

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, ${\sum}_{k=0}^{m}{(-1)}^{k}\left(\genfrac{}{}{0pt}{}{m}{k}\right)\left|\right|{T}^{k}x{\left|\right|}^{p}=0$. 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)....

**Page 1**