### Some Perturbation Results for Analytic Semigroups.

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 aim of this short note is to prove the equivalence of certain definitions of solutions to an evolution variational inequality in metric spaces, introduced by Ambrosio, Gigli, Savaré, and Daneri, Savaré.

Hypercyclicity of -semigroups is a very unstable property: We give examples to show that adding arbitrary small constants or a bounded rank one operator to the generator of a hypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (even in operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limit of nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, the restriction of...

**Page 1**