Open Access

# On a new class of operators related to quasi-Fredholm operators

### 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.

### 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},
}

Coming Soon.