Skew von Neumann constant in Weak Orlicz Spaces and Weak Lebesgue Spaces

TL;DR

This paper introduces and bounds the skew von Neumann constant in weak Orlicz and Lebesgue spaces, expanding understanding of these constants in quasi-Banach spaces.

Contribution

It defines the skew von Neumann constant in quasi-Banach spaces and establishes new bounds within weak Orlicz and Lebesgue spaces.

Findings

Lower bounds for the skew von Neumann constant in weak Orlicz spaces.

Lower bounds for the skew von Neumann - Jordan constant in weak Lebesgue spaces.

Generalization of the skew von Neumann constant and bounds for the p-th von Neumann constant.

Abstract

This paper defines the skew von Neumann constant in quasi-Banach spaces. Meanwhile, we obtain two constants. It presents the upper and lower bounds of two constants. Subsequently, it deduces the lower bound of the skew von Neumann constant within weak Orlicz spaces. Then, leveraging the relationship between weak Orlicz spaces and weak Lebesgue spaces, the lower bound of the skew von Neumann - Jordan constant in weak Lebesgue spaces is established. Meanwhile, in this paper, we also generalize the skew von Neumann constant. Then we present the lower bounds for the $p$-th von Neumann constant in weak Orlicz spaces and weak Lebesgue spaces.