Full paper in PDF:
$%M. Nowak, A generalized mixed topology on Orlicz spaces, Rev. Mat. Univ. Complut. Madrid 7 (1994), no. 1, 2756.%$

A Generalized Mixed Topology on Orlicz Spaces
Marian NOWAK
Institute of Mathematics
Adam Mickiewicz University
Matejki 48/49
60-769 Poznan Poland

Received: October 9, 1992

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

1991 Mathematics Subject Classification: 46E30.