Abstract
Invertibility in Banach algebras generated by two idempotents can be checked with the help of a theorem by Roch, Silbermann, Gohberg, and Krupnik. This theorem cannot be used to study generalized invertibility. The present paper is devoted to group invertibility in two types of finite-dimensional algebras which are generated by two idempotents, algebras generated by two tightly coupled idempotents on the one hand and algebras of dimension at most four on the other. As a side product, the paper gives the classification of all at most four-dimensional algebras which are generated by two idempotents.
Original language | English (US) |
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Pages (from-to) | 715-732 |
Number of pages | 18 |
Journal | Indagationes Mathematicae |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2012 |
Keywords
- Finite-dimensional algebra
- Group inversion
- Idempotent
- Two projections
ASJC Scopus subject areas
- General Mathematics