On concrete models for local operator spaces

TL;DR

This paper introduces a concrete analogue of the space of bounded operators for local operator spaces, using multinormed C*-algebras to extend the classical framework.

Contribution

It proposes a new concrete model, the multinormed C*-algebra, for local operator spaces, expanding the understanding of their structure.

Findings

Defines the multinormed C*-algebra as an analogue of $(H)$ for local operator spaces

Establishes the properties and structure of the proposed model

Provides a foundation for further analysis of local operator spaces

Abstract

In this short note, we propose a concrete analogue of the space $\cL(H)$ for local operator spaces, the multinormed $C^*$-algebra $\displaystyle\prod_{\alpha} \cL(H_{\alpha})$.