Determining Jordan (triple) homomorphisms by invertibility preserving conditions

Abstract

We present a generalized version of Hua’s theorem for Banach algebras, where the condition for all invertible is replaced by for all invertible . We also study linear preservers of inverses along an element, a concept introduced recently that extends some classical concepts of generalized invertibility.

Keywords:

• linear preserver
• generalized inverse
• Banach algebra
• Jordan triple homomorphism

AMS Subject Classifications:

• 47B49; 47B40; 46H05; 15A09

Additional information

Funding

Authors were partially supported by Spanish Ministry of Economy and Competitiveness no. MTM 2011-23843, MTM 2010-17687 and Junta de Andalucía grants FQM 0199, FQM 0194 and FQM 3737. The second author is also supported by a Plan Propio de Investigación grant from University of Almería.