Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
HOUSTON JOURNAL OF MATHEMATICS @ 199.8University ofHouston
 

Summary: HOUSTON JOURNAL OF MATHEMATICS
@ 199.8University ofHouston
Volume 24, No. 1,1998
TWISTED SUMS, FENCHEL-ORLICZ 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 non-trivial
type which can be viewed as Fenchel-Orlicz spaces on R2. We then show that
a large class of Fenchel-Orlicz 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

  

Source: Androulakis, George - Department of Mathematics, University of South Carolina

 

Collections: Mathematics