Operator algebras with contractive approximate identities: Weak   compactness and the spectrum
  We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, `weak compactness' of an operator algebra, or the lack of it, can be seen in the spectra of its elements. 
David P. Blecher and Charles John Read
math.OA math.FA