Vol. 303, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
$L^p$-operator algebras with approximate identities, I

David P. Blecher and N. Christopher Phillips

Vol. 303 (2019), No. 2, 401–457
Abstract

We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on Lp-spaces. In particular we investigate the applicability of the theory of real positivity, which has recently been useful in the study of L2-operator algebras and Banach algebras, to algebras of bounded operators on Lp-spaces. In the process we answer some open questions on real positivity in Banach algebras from work of Blecher and Ozawa.

Keywords
$L^p$-operator algebra, accretive, approximate identity, Banach algebra, Kaplansky density, M-ideal, real positive, smooth Banach space, strictly convex Banach space, state of a Banach algebra, unitization
Mathematical Subject Classification 2010
Primary: 46E30, 46H10, 46H99, 47L10, 47L30
Secondary: 46H35, 47B38, 47B44, 47L75
Milestones
Received: 3 April 2018
Revised: 18 May 2019
Accepted: 19 May 2019
Published: 4 January 2020
Authors
David P. Blecher
Department of Mathematics
University of Houston
Houston, TX
United States
N. Christopher Phillips
Department of Mathematics
University of Oregon
Eugene, OR
United States