On an intrinsic characterization of self-adjoint $C^\ast $-Segal algebras
Volume 145 / 2016
Colloquium Mathematicum 145 (2016), 245-249
MSC: Primary 46H05; Secondary 46K05.
DOI: 10.4064/cm6774-4-2016
Published online: 4 July 2016
Abstract
An intrinsic characterization of self-adjoint $C^\ast $-Segal algebras among Banach $\ast $-algebras is obtained in terms of Pták’s spectral function. A connection between order structure in $C^\ast $-Segal algebras and Grothendieck’s well known dual characterization of $C^\ast $-algebras is revealed.
