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Keywords:
Orlicz spaces; Orlicz-Bochner spaces; Köthe-Bochner spaces; locally solid topologies; generalized mixed topologies; uniformly $\mu$-continuous topologies; inductive limit topologies
Orlicz spaces; Orlicz-Bochner spaces; Köthe-Bochner spaces; locally solid topologies; generalized mixed topologies; uniformly $\mu$-continuous topologies; inductive limit topologies
Summary:
Some class of locally solid topologies (called uniformly $\mu$-continuous) on \linebreak Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly $\mu$-continuous topologies in terms of some family of pseudonorms is given. The finest uniformly $\mu$-continuous topology $\Cal T^\varphi_I(X)$ on the Orlicz-Bochner space $L^\varphi(X)$ is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).
References:
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