 
Summary: HOUSTON JOURNAL OF MATHEMATICS
@ 199.8University ofHouston
Volume 24, No. 1,1998
TWISTED SUMS, FENCHELORLICZ SPACES AND
PROPERTY (M)
G. ANDROULAKIS, C. D. CAZACU AND N. J. KALTON
COMMUNICATED BY GILLES PISIER
ABSTRACT. We study certain twisted sums of Orlics spaces with nontrivial
type which can be viewed as FenchelOrlicz spaces on R2. We then show that
a large class of FenchelOrlicz spaces on R" can be renormed to have property
(M). In particular this gives a new construction of the twisted Hilbert space
22 and shows it has property (M), after an appropriate renorming.
1. INTRODUCTION
A twisted sum 2 of two Banach spaces X and Y is defined (see [ll]) through
a short exact sequence: 0 + X + Z + Y + 0. These short exact se
quences in the category of (quasi)Banach spaces are considered naturally in the
investigation of three space properties (a property P in the category of quasi
Banach spaces is called a three space property if for every short exact sequence
as above, 2 has property P whenever X and Y have it). The roots of this the
ory go to Enflo, Lindenstrauss and Pisier's solution [3] to Palais' problem: the
