On k-Quasi-(m, n, C)-Isosymmetric Operators

Year 2024, Early Access, 1 - 13

Khadija Gherairi , Nouf Maqbul Saqer Alruwaili , Sid Ahmed Ould Ahmedmahmoud

https://doi.org/10.15672/hujms.1333379

Abstract

We study the set of k-quasi-(m, n,C)-isosymmetric operators. This family extends the
set of (m, , n,C)-isosymmetric operators. In the present article, we give operator matrix
representation of k-quasi-(m, , n,C)-isosymmetric operator in order to obtain some structural
properties for such operators. we show that if R is k-quasi-(m, n,C)-isosymmetric,
then Rq is a k-quasi-(m, n,C)-isosymmetric operator. We show that the product of an
k1-quasi-(m1, n1,C)-isosymmetric and an n2-quasi-(m2, n2,C)-isosymmetric which are Cdouble
commuting is an max{k1, k2}-quasi-(m1 + m2 − 1, n1 + n2 − 1,C)-isosymmetry
under suitable conditions. In particular, we prove the stability of perturbation of kquasi-(
m, n,C)-isosymmetric operator by a nilpotent operator of order p under suitable
conditions. Moreover, we give some results about the joint approximate spectrum of a
k-quasi-(m, n,C)-isosymmetric operators.

Keywords

$m$-isometries, $n$-quasi-$m$-isometries, $m$-isometric tuple, joint approximate spectrum

Supporting Institution

the Deanship of Scientific Research at Jouf University

Project Number

(DSR-2021-03-0337)

References

• [1] A. Abeer, O.A. Mahmoud Sid Ahmed and B.A. Farsin, n-quasi-m-complex symmetric operators, Symmetry 15 (9), 1662, 2023.