L^p operator algebras with approximate identities I

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.

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

References in corpus (1)

• Quotients of Banach algebras acting on $L^p$-spaces

Cited by in corpus (5)

• Rigidity results for $L^p$-operator algebras and applications
• Multiplier algebras of $L^p$-operator algebras
• Banach algebras associated to twisted étale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces
• $L^p$-spectral triples and $p$-quantum compact metric spaces
• $L^p$-modules and $L^p$-correspondences