A-Numerical Radius and Product of Semi-Hilbertian Operators

Zamani, Ali

doi:10.1007/s41980-020-00388-4

Cited by 14 publications

(11 citation statements)

References 13 publications

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“…Remark 2.9. Very recently, as our work was in progress, the above lemma has been proved by Zamani in [19]. Our proof here is different from his approach.…”

Section: A-numerical Radius Orthogonality and Parallelismmentioning

confidence: 77%

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

Bhunia

Feki

Paul

2020

Bull. Iran. Math. Soc.

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In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space H which are bounded with respect to the semi-norm induced by a positive operator A on H. Moreover, a characterization of the A-numerical radius parallelism for A-rank one operators is proved. As applications of the obtained results, we obtain some A-numerical radius inequalities of operator matrices where A is the operator diagonal matrix with diagonal entries are positive operator A. Some other related results are also investigated.

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“…Remark 2.9. Very recently, as our work was in progress, the above lemma has been proved by Zamani in [19]. Our proof here is different from his approach.…”

Section: A-numerical Radius Orthogonality and Parallelismmentioning

confidence: 77%

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

Bhunia

Feki

Paul

2020

Bull. Iran. Math. Soc.

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“…Proof The first two statements can be found in [4]. The third statement follows from [27,Proposition 2.4].…”

Section: For Any T ∈ B a 1∕2 (H) We Have T(n(a)) ⊂ N(a) And Cl(w A (T)) = Cl(w( T))mentioning

confidence: 99%

Essential numerical ranges of operators in semi-Hilbertian spaces

Baklouti

Mabrouk

2021

Ann. Funct. Anal.

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Let A be a positive bounded operator on an infinite dimensional complex and separable Hilbert space (H, ⟨, ⟩) and ∶=B(H)∕K(H) be the Calkin algebra and ′ its dual; here K(H) denotes the closed ideal of B(H) consisting of all compact operators on H . For an operator T on H , let ‖T‖ A and V A (T) denote the A-operator semi-norm and the A-numerical range induced by A. The A-essential numerical range and the A-essential norm of T are defined by V e A (T) = V Â( T) andwhereIn this paper, we establish some properties of the A-essential numerical range.In particular we show that if T has an A-adjoint then

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“…In 2019, Moslehian et al [20] again continued the study of A-numerical radius and established some inequalities for A-numerical radius. Further generalizations and refinements of A-numerical radius are discussed in [5,6,22,29]. In 2020, Bhunia et al [8] obtained several A-numerical radius inequalities.…”

Section: Letmentioning

confidence: 99%

On A-numerical radius inequalities for 2 x 2 operator matrices-II

Sahoo

2021

Filomat

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Rout et al. [Linear Multilinear Algebra 2020, DOI: 10.1080/03081087.2020.1810201] presented certain A-numerical radius inequalities for 2x2 operator matrices and further results on A-numerical radius of certain 2x2 operator matrices are obtained by Feki [Hacet. J. Math. Stat., 2020, DOI:10.15672/hujms.730574], very recently. The main goal of this article is to establish certain A-numerical radius equalities for operator matrices. Several new upper and lower bounds for the A-numerical radius of 2 x 2 operator matrices has been proved, where A be the 2 x 2 diagonal operator matrix whose diagonal entries are positive bounded operator A. Further, we prove some refinements of earlier A-numerical radius inequalities for operators.

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A-Numerical Radius and Product of Semi-Hilbertian Operators

Cited by 14 publications

References 13 publications

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

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

Essential numerical ranges of operators in semi-Hilbertian spaces

On A-numerical radius inequalities for 2 x 2 operator matrices-II

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