Semi-simplicity of some semi-prime Banach algebras.
Some observations concerning the non-existence of bounded differentials on weighted algebras.
Spectral isometries
In this survey, we summarise some of the recent progress on the structure of spectral isometries between C*-algebras.
Stability of commuting maps and Lie maps
Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
Stability of multipliers on Banach algebras.