Scaled-free objects II
Abstract
This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps completely bounded on a generation set to a completely bounded linear map of the matrix-normed space. Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods.
Cite
@article{arxiv.1405.7113,
title = {Scaled-free objects II},
author = {Will Grilliette},
journal= {arXiv preprint arXiv:1405.7113},
year = {2017}
}
Comments
46 pages. Version 4 fixed a few minor typos. Version 3 added matricial completion; fixed an arithmetic error in Example 3.5.10. Version 2 added a preliminaries section on weighted sets and matricial Banach spaces, incorporating much of "Matricial Banach spaces" in summary; fixed a domain issue in Lemma 3.3.2; simplified Examples 3.5.10 and 4.11; added more proofs to Sections 4 and 5