Djilali BEKAİ, Benali ABDELKADER, Hakem ALI

On the Classes of (n, m) Power (D, A)-Normal and (n,m) Power (D, A)-Quasinormal Operators in Semi-Hilbertian Space

The concept of (?, ?) power ?-normal operators on Hilbertian space is defined by Ould Ahmed Mahmoud Sid Ahmed and Ould Beinane Sid Ahmed in [1]. In this paper we introduce a new classes of operators on semi-Hilbertian space (ℋ, ∥. ∥?) called (?, ?) power-(?, ?)-normal denoted [(?, ?)??]? and (?, ?) power-(?, ?)-quasi-normal denoted [(?, ?)???]? associated with a Drazin invertible operator using its Drazin inverse. Some properties of [(?, ?)??]? and [(?, ?)???]? are investigated and some examples are also given. An operator ? ∈ ℬ? (ℋ) is said to be (n, m) power-(?, ?)- normal for some positive operator ? and for some positive integers ? and ? if (??)?(?⋕)? = (?⋕)?(??)?.

Keywords:

A-positive, A-isometry, Semi-Hilbertian space, A-positive A-isometry, A-normal, A-quasi-normal,

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Cankaya University Journal of Science and Engineering-Cover

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2009
Yayıncı: Çankaya Üniversitesi

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