Structures of left $n$-invertible operators and their applications

Caixing Gu¹

¹ Department of Mathematics California Polytechnic State University San Luis Obispo, CA 93407, U.S.A.

Studia Mathematica, Tome 226 (2015) no. 3, pp. 189-211

Résumé

We study left $n$-invertible operators introduced in two recent papers. We show how to construct a left $n$-inverse as a sum of a left inverse and a nilpotent operator. We provide refinements for results on products and tensor products of left $n$-invertible operators by Duggal and Müller (2013). Our study leads to improvements and different and often more direct proofs of results of Duggal and Müller (2013) and Sid Ahmed (2012). We make a conjecture about tensor products of left $n$-invertible operators and prove this conjecture in several cases. Finally, applications of these results are given to left $n$-invertible elementary operators and essentially left $n$-invertible operators.

Détail

DOI : 10.4064/sm226-3-1

Keywords: study n invertible operators introduced recent papers construct n inverse sum inverse nilpotent operator provide refinements results products tensor products n invertible operators duggal ller study leads improvements different often direct proofs results duggal ller sid ahmed make conjecture about tensor products n invertible operators prove conjecture several cases finally applications these results given n invertible elementary operators essentially n invertible operators