Real positivity and approximate identities in Banach algebras

Abstract

Blecher and Read have recently introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^{\ast }$-algebraic results and theories to more general algebras. In the present paper we generalize some part of this, and some other facts, to larger classes of Banach algebras.

47 pages. A final revision. To appear Pacific J. Math

References in corpus (6)

• The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
• Noncommutative peak interpolation revisited
• On positivity and roots in operator algebras
• Normality of spaces of operators and quasi-lattices
• Operator algebras with contractive approximate identities, III
• Generalization of C*-algebra methods via real positivity for operator and Banach algebras

Cited by in corpus (7)

• L^p operator algebras with approximate identities I
• Completely contractive projections on operator algebras
• Generalization of C*-algebra methods via real positivity for operator and Banach algebras
• Characterizations of ordered operator spaces
• Jordan operator algebras revisited
• Roots in operator and Banach algebras
• Jordan operator algebras: Basic theory