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A Course In Functional Analysis

A-numerical radius inequalities for semi-Hilbertian space operators

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.

Spectral radius of semi-Hilbertian space operators and its applications

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

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 $${\mathcal {H}}.$$

A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications

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...

Joint normality of operators in semi-Hilbertian spaces

In this paper we generalize the concept of Davis–Wielandt shell of operators on a Hilbert space when a semi-inner product induced by a positive operator A is considered. Moreover, we investigate the parallelism of A-bounded operators with respect to the seminorm and the numerical radius induced by A. Mainly, we characterize A-normaloid operators in terms of their A-Davis–Wielandt radii. In addition, a connection between A-seminorm-parallelism to the identity operator and an equality condition for the A-Davis–Wielandt radius is proved. This generalizes the well-known results in Chan and Chan (Oper Matrices 11(3):885–890, 2017), Zamani et al. (Linear Multilinear Algebra 67(11):2147–2158, 2019). Some other related results are also discussed.

Davis–Wielandt shells of semi-Hilbertian space operators and its applications

In this paper we generalize the concept of Davis-Wielandt shell of operators on a Hilbert space when a semi-inner product induced by a positive operator $A$ is considered. Moreover, we investigate the parallelism of $A$-bounded operators with respect to the seminorm and the numerical radius induced by $A$. Mainly, we characterize $A$-normaloid operators in terms of their $A$-Davis-Wielandt radii. In addition, a connection between $A$-seminorm-parallelism to the identity operator and an equality condition for the $A$-Davis-Wielandt radius is proved. This generalizes the well-known results in \cite{zamanilma2018,chanchan}. Some other related results are also discussed.

Davis-Wielandt shells of semi-Hilbertian space operators and its applications

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L1-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

In this paper, we introduce the class of n-quasi- ( m , C ) -isometric operator on a Hilbert space which is a variation of ( m , C ) -isometric operators Chō M, Ko E, Lee JE. [On ( m , C ) -isometr...

Sid Ahmed Ould Ahmed Mahmoud

Papers

Joint normality of operators in semi-Hilbertian spaces

Davis–Wielandt shells of semi-Hilbertian space operators and its applications

Davis-Wielandt shells of semi-Hilbertian space operators and its applications

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

On n-quasi-(m,C)-isometric operators