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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3426

Abstract

We introduce the class of $(M, k)$-quasi-$*$-paranormal operators on a Hilbert space $H$. This class extends the classes of $*$-paranormal and $k$-quasi-$*$-paranormal operators. An operator $T$ on a complex Hilbert space is called $(M, k)$-quasi-$*$-paranormal if there exists $M>0$ such that \begin{equation*} \sqrt{M}\left\Vert T^{k+2}x\right\Vert \left\Vert T^{k}x\right\Vert \geq \left\Vert T^{\ast }T^{k}x\right\Vert ^{2} \end{equation*} for all $x\in H.$ In the present article, we give operator matrix representation of a $(M, k)$-quasi-$*$-paranormal operator. The compactness, the invariant subspace, and some topological properties of this class of operators are studied. Several properties of this class of operators are also presented.

Keywords

$M$ -*-paranormal operator, $(M, k)$ -quasi-*-paranormal operator, SVEP, invariant subspacce

First Page

1267

Last Page

1275

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