Quotients, $\ell_\infty$ and abstract Ces\`aro spaces

TL;DR

This paper explores the properties of quotient spaces and their relation to the existence of lattice isometric copies of _ in abstract Cesro spaces, advancing understanding of their structure.

Contribution

It characterizes conditions under which abstract Cesro spaces contain a lattice isometric copy of _, linking quotient space properties to space embeddings.

Findings

Identifies properties of $X$ that guarantee _ embeddings in $CX$

Analyzes re-arrangement properties of the norm in quotient spaces $X/X_a$

Determines conditions for the existence of lattice isometric copies of _ in $CX$

Abstract

Investigating some re-arrangement properties of the norm in the quotient spaces $X/X_a$ we determine the properties of the spaces $X$ guaranteeing the existence of a lattice isometric copy of $\ell_\infty$ in the abstract Ces\`aro spaces $CX$.