Injectivity and projectivity in $p$-multinormed spaces

TL;DR

This paper characterizes large classes of injective and projective $p$-multinormed spaces, demonstrating their universality and showing that any such space can be embedded into a quotient of a Banach lattice.

Contribution

It introduces classes of injective and projective $p$-multinormed spaces that are universal and provides a canonical representation for all $p$-multinormed spaces.

Findings

Large classes of injective and projective $p$-multinormed spaces identified.

Every $p$-multinormed space embeds into a quotient of an injective or projective space.

Any $p$-multinormed space can be represented as a subspace of a quotient of a Banach lattice.

Abstract

We find large classes of injective and projective $p$-multinormed spaces. In fact, these classes are universal, in the sense that every $p$-multinormed space embeds into (is a quotient of) an injective (resp. projective) $p$-multinormed space. As a consequence, we show that any $p$-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice.