IJPAM: Volume 38, No. 3 (2007)

EXTENSION OF NORMS RELATED TO FULLY
$K$-ROTUND NORMS AND MIDPOINT LOCALLY
UNIFORMLY ROTUND NORMS

Yanzheng Duan$^1$, Bor-Luh Lin$^2$
$^{1,2}$Department of Mathematics
The University of Iowa
Iowa City, IA 52242-1419, USA
$^1$e-mail: yduan@math.uiowa.edu
$^2$e-mail: bllin@math.uiowa.edu


Abstract.In this paper, we prove that fully $k$-rotund (respectively, locally fully $k$-rotund, fully $\omega
$-rotund, fully locally $\omega
$-rotund, locally mean $k$-rotund and midpoint locally uniformly rotund) norms can be extended from a closed subspace of a Banach space to the whole space.

Received: April 10, 2007

AMS Subject Classification: 46B03, 46B20

Key Words and Phrases: rotund extension, fully $k$-rotund spaces, locally fully $k$-rotund spaces, fully $\omega
$-rotund spaces, locally fully $\omega
$-rotund spaces, locally mean $k$-rotund spaces, midpoint locally uniformly rotund spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 3