Witold Wnuk

Landau type theorem for Orlicz spaces

In this paper the authors discuss Landaus theorem presenting an inverse of the classical Holder-type inequality for sequence and function spaces.The results given are for Orlicz spaces and their g ...

Orlicz spaces cannot be normed analogously to Lp-spaces

Using the multipliers of an Orlicz function F we show that the functional PG,F(X)=G(∫SF(|x(s)|)dμ) , defined on the Orlicz space LF(μ), is homogeneous if and only if F(r) = F(1)rp and G(r) = G(1)r1/p for some p>0 and all r≥0. This statement is proved under very general assumptions about the measure μ.

On the Levi and Lebesgue properties

Abstract The paper is devoted to a question if the Levi property is preserved by direct sums and quotients. The three-space problem for the Levi and Lebesgue properties in topological Riesz spaces is also investigated.