Author
Kais Feki
Other affiliations: University of Monastir
Bio: Kais Feki is an academic researcher from University of Sfax. The author has contributed to research in topics: Hilbert space & Bounded function. The author has an hindex of 10, co-authored 30 publications receiving 293 citations. Previous affiliations of Kais Feki include University of Monastir.
Papers
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TL;DR: In this article, the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space was investigated, and it was shown that these sets are convex for d ≥ 2.
84 citations
TL;DR: In this paper, the spectral radius of bounded linear operators acting on a complex Hilbert space was introduced, which are bounded with respect to the seminorm induced by a positive operator A on the complex space.
Abstract: In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $$\mathcal {H}$$
, which are bounded with respect to the seminorm induced by a positive operator A on $$\mathcal {H}$$
. Mainly, we show that $$r_A(T)\le \omega _A(T)$$
for every A-bounded operator T, where $$r_A(T)$$
and $$\omega _A(T)$$
denote respectively the A-spectral radius and the A-numerical radius of T. This allows to establish that $$r_A(T)=\omega _A(T)=\Vert T\Vert _A$$
for every A-normaloid operator T, where $$\Vert T\Vert _A$$
is denoted to be the A-operator seminorm of T. Moreover, some characterizations of A-normaloid and A-spectraloid operators are given.
58 citations
TL;DR: In this article, the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space was introduced, where an additional semi-inner product induced by a positive operato...
Abstract: In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space H when an additional semi-inner product induced by a positive operato...
48 citations
TL;DR: In this paper, the numerical radius orthogonality of operators on a complex Hilbert space is characterized, and a characterization of the A-numerical radius parallelism for A-rank one operators is obtained.
Abstract: In this paper, we aim to introduce and characterize the numerical radius orthogonality of operators on a complex Hilbert space $${\mathcal {H}}$$
which are bounded with respect to the seminorm induced by a positive operator A on $${\mathcal {H}}$$
. Moreover, a characterization of the A-numerical radius parallelism for A-rank one operators is obtained. As applications of the results obtained, we derive some $${\mathbb {A}}$$
-numerical radius inequalities of operator matrices, where $${\mathbb {A}}$$
is the operator diagonal matrix whose each diagonal entry is a positive operator A on a complex Hilbert space $${\mathcal {H}}.$$
39 citations
TL;DR: In this article, an alternative proof of a recent result proved in Moslehian et al. (Linear Algebra Appl 591:299-321 2020) is given.
Abstract: Let A be a positive bounded linear operator acting on a complex Hilbert space
$${\mathcal {H}}$$
. Our aim in this paper is to prove some A-numerical radius inequalities of bounded linear operators acting on
$${\mathcal {H}}$$
when an additional semi-inner product structure induced by A is considered. In particular, an alternative proof of a recent result proved in Moslehian et al. (Linear Algebra Appl 591:299–321 2020) is given.
36 citations
Cited by
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TL;DR: In this article, the authors prove upper and lower bounds for the A-numerical radius of a positive bounded operator in semi-Hilbertian spaces. But they do not consider the case where the operator T is a distinguished A-adjoint operator of A. In particular, they show that w A (T ) ≤ w A(T ), where | cos | denotes the A cosine of angle of T.
66 citations
TL;DR: In this paper, the spectral radius of bounded linear operators acting on a complex Hilbert space was introduced, which are bounded with respect to the seminorm induced by a positive operator A on the complex space.
Abstract: In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $$\mathcal {H}$$
, which are bounded with respect to the seminorm induced by a positive operator A on $$\mathcal {H}$$
. Mainly, we show that $$r_A(T)\le \omega _A(T)$$
for every A-bounded operator T, where $$r_A(T)$$
and $$\omega _A(T)$$
denote respectively the A-spectral radius and the A-numerical radius of T. This allows to establish that $$r_A(T)=\omega _A(T)=\Vert T\Vert _A$$
for every A-normaloid operator T, where $$\Vert T\Vert _A$$
is denoted to be the A-operator seminorm of T. Moreover, some characterizations of A-normaloid and A-spectraloid operators are given.
58 citations
TL;DR: In this article, the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space was introduced, where an additional semi-inner product induced by a positive operato...
Abstract: In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space H when an additional semi-inner product induced by a positive operato...
48 citations
TL;DR: In this paper, the authors give necessary and sufficient conditions for two orthogonal semi-Hilbertian operators to satisfy Pythagoras' equality and derive new upper and lower bounds for the numerical radius of operators.
47 citations
TL;DR: In this paper, the numerical radius orthogonality of operators on a complex Hilbert space is characterized, and a characterization of the A-numerical radius parallelism for A-rank one operators is obtained.
Abstract: In this paper, we aim to introduce and characterize the numerical radius orthogonality of operators on a complex Hilbert space $${\mathcal {H}}$$
which are bounded with respect to the seminorm induced by a positive operator A on $${\mathcal {H}}$$
. Moreover, a characterization of the A-numerical radius parallelism for A-rank one operators is obtained. As applications of the results obtained, we derive some $${\mathbb {A}}$$
-numerical radius inequalities of operator matrices, where $${\mathbb {A}}$$
is the operator diagonal matrix whose each diagonal entry is a positive operator A on a complex Hilbert space $${\mathcal {H}}.$$
39 citations