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.