The concept of (𝑛, 𝑚) power 𝐷-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, ∥. ∥𝐴) called (𝑛, 𝑚) power-(𝐷, 𝐴)-normal denoted [(𝑛, 𝑚)𝐷𝑁]𝐴 and (𝑛, 𝑚) power-(𝐷, 𝐴)-quasi-normal denoted [(𝑛, 𝑚)𝐷𝑄𝑁]𝐴 associated with a Drazin invertible operator using its Drazin inverse. Some properties of [(𝑛, 𝑚)𝐷𝑁]𝐴 and [(𝑛, 𝑚)𝐷𝑄𝑁]𝐴 are investigated and some examples are also given. An operator 𝑇 ∈ ℬ𝐴 (ℋ) is said to be (n, m) power-(𝐷, 𝐴)- normal for some positive operator 𝐴 and for some positive integers 𝑛 and 𝑚 if (𝑇𝐷)𝑛(𝑇⋕)𝑚 = (𝑇⋕)𝑚(𝑇𝐷)𝑛.
A-positive A-isometry Semi-Hilbertian space A-positive A-isometry A-normal A-quasi-normal
The authors would like to express their gratitude to the referee. We are very grateful for his help, his careful observations, and his careful reading, which led to the improvement of the article.
Birincil Dil | İngilizce |
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Konular | Mühendislik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Kasım 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 18 Sayı: 2 |