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