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Local structure of generalized Orlicz−Lorentz function spaces

Kolwicz P.

Commentationes Mathematicae

2015

Vol 55, No. 2

211--227

We study the local structure of a separated point x in the generalized Orlicz-Lorentz space Λφ which is a symmetrization of the respective Musielak-Orlicz space Lφ. We present criteria for an LM point and a UM point, and sufficient conditions for a point of order continuity and an LLUM point, in the space Λφ. We prove also a characterization of strict monotonicity of the space Λφ .

Relations between various continuity concepts in effect algebras

Khare M., Gupta S.

Demonstratio Mathematica

2008

Vol. 41, nr 3

507-518

The aim of the present paper is to establish relations between continuity concepts for a nonnegative extended real-valued function [...] defined on an effect algebra. Examples and counterexamples are given to illustrate various situations arising in this study.

On the smallest singular seminorm in a class of normed Köthe function spaces

Hudzik H., Baoxiang Wang Baoxiang

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

43-52

Let X be a normed Köthe function space and let us denote by Fx the set of all singular support functionals at x. Then px(y) =sup{|(f,y)|:f