$$(\alpha ,\beta )$$-A-Normal operators in semi-Hilbertian spaces

Benali, Abelkader; Mahmoud, Sid Ahmed Ould Ahmed

doi:10.1007/s13370-019-00690-3

Cited by 3 publications

(4 citation statements)

References 12 publications

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“…We call such elements as neutral elements of SIP space. SIP space also known as semi-Hilbertian space ( [1], [4], [5]) or semi-unitary space [7]. SIP had been applied for the solution of general quadratic programming [14], also as a representation of quiver [7].…”

Section: Introductionmentioning

confidence: 99%

“…SIP had been applied for the solution of general quadratic programming [14], also as a representation of quiver [7]. Latest studies on SIP showed the generalization of concepts in IP space to SIP space, such as properties of normal operators ( [11], [5]), isometry and unitary properties [1], and closed operator [4]; also, geometrical aspects, such as metric on projections [2], Birkhoff-James orthogonality ( [17], [12]) and numerical radius ( [8], [6], [13]).…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, we derive Generalized Riesz Representation Theorem in SIP spaces. Arias et.al [1] gave one distinguished adjoint operator in SIP which lead to the discoveries of some properties of normal operator ( [11], [5], [15]). Here, we give the description of all adjoint operators of a bounded linear operator on SIP space.…”

Section: Introductionmentioning

confidence: 99%

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On The Adjoint of Bounded Operators On A Semi-Inner Product Space

Respitawulan,

Pangestu,

Yuliawan

et al. 2023

JIMS

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The notion of semi-inner product (SIP) spaces is a generalization of inner product (IP) spaces notion by reducing the positive definite property of the product to positive semi-definite. As in IP spaces, the existence of an adjoint of a linear operator on a SIP space is guaranteed when the operator is bounded. However, in contrast, a bounded linear operator on SIP space can have more than one adjoint linear operators. In this article we give an alternative proof of those results using the generalized Riesz Representation Theorem in SIP space. Further, the description of all adjoint operators of a bounded linear operator in SIP space is identified.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On The Adjoint of Bounded Operators On A Semi-Inner Product Space

Respitawulan,

Pangestu,

Yuliawan

et al. 2023

JIMS

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“…For α 1, we observe that T * is hyponormal and for β 1, we obtain that T is hyponormal. Interested readers can nd more details on (α, β)-normal operators in [4][5][6][7][8][9]. e concept of p-(α, β)-normal operators was introduced by Senthilkumar and Shanthi [10].…”

Section: Introductionmentioning

confidence: 99%

$(α, β)$ -Normal Operators in Several Variables

Mahmoud

Himadan

Sarosh

2022

Mathematical Problems in Engineering

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We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormality to joint quasi-hyponormality.

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