Core inverse in Banach algebras. (English) Zbl 1453.46045
Summary: We define and characterize the core inverse in the context of Banach algebras. The Banach space operator case is also considered. Using the core inverse, we present new characterizations of EP Banach space operators and EP Banach algebra elements. The dual core inverse for Banach algebra elements is presented too. Some new characterizations of co-EP Banach algebra elements are given by means the core inverse and dual core inverse.
MSC:
| 46H05 | General theory of topological algebras |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
| 15A09 | Theory of matrix inversion and generalized inverses |
References:
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