[Banach] Abstract of a paper by Jan-David Hardtke

This is an announcement for the paper "On certain Opial-type results in Ces`aro spaces of vector-valued functions" by Jan-David Hardtke.

Abstract: Given a Banach space $X$, we consider Ces`aro spaces $\text{Ces}_p(X)$ of $X$-valued functions over the interval $[0,1]$, where $1\leq p<\infty$. We prove that if $X$ has the Opial/uniform Opial property, then certain analogous properties also hold for $\text{Ces}_p(X)$. We also prove a result on the Opial/uniform Opial property of Ces`aro spaces of vector-valued sequences.

Archive classification: math.FA

Mathematics Subject Classification: 46E40 46E30 46B20

Remarks: 15 pages, partial text overlap with arXiv:1403.2647

Submitted from: hardtke@math.fu-berlin.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1509.08097

or

http://arXiv.org/abs/1509.08097