L^p operator algebras with approximate identities I
Functional Analysis
2020-01-08 v2 Mathematical Physics
math.MP
Operator Algebras
Abstract
We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on L^p spaces. In particular we investigate the applicability of the theory of real positivity, which has recently been useful in the study of L^2-operator algebras and Banach algebras, to algebras of bounded operators on Lp spaces.
Cite
@article{arxiv.1802.04424,
title = {L^p operator algebras with approximate identities I},
author = {David P. Blecher and N. Christopher Phillips},
journal= {arXiv preprint arXiv:1802.04424},
year = {2020}
}
Comments
46 pages, Material from this paper and its sequel were presented at 2017 conferences in Houston (August), the East Coast Operator Algebras Symposium, and the SAMS congress. To appear Pacific J Math