Full paper in PDF:

$%M. Nowak, A generalized mixed topology on Orlicz spaces, Rev. Mat. Univ. Complut. Madrid 7
(1994), no. 1, 27–56.%$

A Generalized Mixed Topology on Orlicz
Spaces

Marian NOWAK

Institute of Mathematics

Adam Mickiewicz University

Matejki 48/49

60-769 Poznan — Poland

Adam Mickiewicz University

Matejki 48/49

60-769 Poznan — Poland

ABSTRACT

Let be an Orlicz space defined by an arbitrary Orlicz function over a positive measure space and provided with its usual F-norm . In a natural convergence can be defined as follows: a sequence in is said to be -convergent to whenever () and . In this paper we examine some kind of generalized inductive-limit topology (in the sense of Turpin) in that generates our -convergence in . The main aim of the paper is to obtain a description of the topology in terms of some family of F-norms defined by other Orlicz functions. As an application we obtain a topological characterization of the -convergence in .

1991 Mathematics Subject Classification: 46E30.