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$L^p$-operator
algebras with approximate identities, I
David P. Blecher and N. Christopher Phillips |
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Vol. 303 (2019), No. 2, 401–457
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Abstract |
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We initiate an investigation into how much the existing theory of (nonselfadjoint) operator algebras on a Hilbert space generalizes to algebras acting on -spaces. In particular we investigate the applicability of the theory of real positivity, which has recently been useful in the study of -operator algebras and Banach algebras, to algebras of bounded operators on -spaces. In the process we answer some open questions on real positivity in Banach algebras from work of Blecher and Ozawa. |
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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
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Mathematical Subject Classification 2010
Primary: 46E30, 46H10, 46H99, 47L10, 47L30
Secondary: 46H35, 47B38, 47B44, 47L75
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Milestones
Received: 3 April 2018
Revised: 18 May 2019
Accepted: 19 May 2019
Published: 4 January 2020
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Authors |
| David P. Blecher | |
| Department of Mathematics University of Houston Houston, TX United States |
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| N. Christopher Phillips | |
| Department of Mathematics University of Oregon Eugene, OR United States |
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