Abstract
In this paper, we introduce a generalization of quasi-Fredholm
operators [7] to $k$-quasi-Fredholm operators on Hilbert
spaces for nonnegative integer $k$. The case when $k = 0,$
represents the set of quasi-Fredholm operators and the meeting of
the classes of $k$-quasi-Fredholm operators is called the class of
pseudo-quasi-Fredholm operators. We present some fundamental
properties of the operators belonging to these classes and, as
applications, we prove some spectral theorem and finite-dimensional
perturbations results for these classes. Also, the notion of new
index of a pseudo-quasi-Fredholm operator called $pq$-index is
introduced and the stability of this index by finite-dimensional
perturbations is proved. This paper extends some results proved in
[5] to closed unbounded operators.
Key words: Complex Volterra operator, symbol, BMOA, spectrum.
Full Text
Article Information
| Title | On a new class of operators related to quasi-Fredholm operators |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 2, 141-166 |
| DOI | 10.31392/MFAT-npu26_2.2020.06 |
| MathSciNet |
MR4127611 |
| Milestones | Received 21.04.2019; Revised 02.01.2020 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
Zied Garbouj
Institut Superieur des Sciences Appliquees et de Technologie de Kairouan, Departement de Mathematiques, Avenue Beit El Hikma, 3100 Kairouan, Tunisia
Haïkel Skhiri
Institut Superieur des Sciences Appliquees et de Technologie de Kairouan, Departement de Mathematiques, Avenue Beit El Hikma, 3100 Kairouan, Tunisia
Citation Example
Zied Garbouj and Haïkel Skhiri, On a new class of operators related to quasi-Fredholm operators, Methods Funct. Anal. Topology 26
(2020), no. 2, 141-166.
BibTex
@article {MFAT1346,
AUTHOR = {Zied Garbouj and Haïkel Skhiri},
TITLE = {On a new class of operators related to quasi-Fredholm operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {2},
PAGES = {141-166},
ISSN = {1029-3531},
MRNUMBER = {MR4127611},
DOI = {10.31392/MFAT-npu26_2.2020.06},
URL = {http://mfat.imath.kiev.ua/article/?id=1346},
}
