Metric and topological freedom for operator sequence spaces

TL;DR

This paper characterizes free and cofree objects in the category of operator sequence spaces, establishing duality theory similar to normed spaces and providing a comprehensive description of these objects.

Contribution

It introduces a duality framework for operator sequence spaces and fully describes their free and cofree objects, advancing the understanding of their structure.

Findings

Duality theory for operator sequence spaces established

Complete description of metrically free objects

Complete description of topologically cofree objects

Abstract

In this paper we give description of free and cofree objects in the category of operator sequence spaces. First we show that this category possess the same duality theory as category of normed spaces, then with the aid of these results we give complete description of metrically and topologically free and cofree objects.