Emiel Lorist
(Delft University of Technology)
Let be a bounded operator on
and
be a Banach space. We ask the question when the prescription
extends by linearity to a bounded operator on the Bochner space
. Operators of this form play, for example, an important role in the analysis of parabolic partial differential equations from an evolution equation perspective. In this talk I will first thoroughly introduce the
-extension problem and prove a few elementary sufficient conditions on
and
for which the
-extension problem has an affirmative answer. Moreover I will give some simple counterexamples. Towards the end of the talk I will state a few more recent results related to the
-extension problem, which come from my own research.