Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 4 (2016), 609-621.
On -generalized invertible operators on Banach spaces
A bounded linear operator on a Banach space is called an -left generalized inverse of an operator for a positive integer if
and it is called an -right generalized inverse of if
If is both an -left and an -right generalized inverse of , then it is said to be an -generalized inverse of .
This paper has two purposes. The first is to extend the notion of generalized inverse to -generalized inverse of an operator on Banach spaces and to give some structure results. The second is to generalize some properties of -partial isometries on Hilbert spaces to the class of -left generalized invertible operators on Banach spaces. In particular, we study some cases in which a power of an -left generalized invertible operator is again -left generalized invertible.
Ann. Funct. Anal., Volume 7, Number 4 (2016), 609-621.
Received: 13 March 2016
Accepted: 3 May 2016
First available in Project Euclid: 23 September 2016
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Ezzahraoui, Hamid. On $m$ -generalized invertible operators on Banach spaces. Ann. Funct. Anal. 7 (2016), no. 4, 609--621. doi:10.1215/20088752-3660801. https://projecteuclid.org/euclid.afa/1474652185