On positivity and roots in operator algebras

Abstract

In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present paper consists of complements to some facts in the just mentioned papers, concerning this notion of positivity. For example we prove a result on the numerical range of products of the roots of commuting operators with numerical range in a sector.

11 pages, to appear Integral Equations Operator Theory

References in corpus (2)

• Noncommutative peak interpolation revisited
• Operator algebras with contractive approximate identities, III

Cited by in corpus (7)

• Real positivity and approximate identities in Banach algebras
• Completely contractive projections on operator algebras
• Generalization of C*-algebra methods via real positivity for operator and Banach algebras
• Characterizations of ordered operator spaces
• Contractive projections and real positive maps on operator algebras
• Roots in operator and Banach algebras
• Jordan operator algebras: Basic theory