Meromorphic functional calculus and local spectral theory.
Chain-finite operators and locally chain-finite operators.
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).
Acotabilidad de la función resolvente local.
On Neumann operators.
Almost regular operators are regular.
De conejos y números. La sorprendente sucesión de Fibonacci.
Operators with an ergodic power
We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
On operators T such that f(T) is hypercyclic.
Local ergodic theorems.
Stability of the local spectrum.
On the poles of the local resolvent.
Properties and applications of the local functional calculus.
Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces
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...
Powers of m-isometries
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, . 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 and are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if is an (m,p)-isometry and is an (l,p)-isometry, then is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l)....
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