Some properties of 𝑝-limited sets

Abstract

Karn and Sinha [Glasg. Math. J. 56 (2014), pp. 427–437] introduced the p p -limited ( 1 ≤ p > ∞ 1 \leq p > \infty ) sets (see the definition below). We show that p p -limited sets are preserved by continuous polynomials as well as by the projective tensor product and that scalar-valued polynomials are p p -summable on p p -limited sets. Considering the notion of p p -limited set from the ℓ p \ell _p -valued operators point of view, we introduce in Section \ref{sec:3} two weaker types of p p -limitedness in the setting of Banach lattices and study their basic properties.