Open AccessThe class of (n,m)power-A-quasi-hyponormal operators in semi-Hilbertian space
Author(s) -
Djilali Bekai,
Abdelkader Benali,
Ali Hakem
Publication year - 2021
Publication title -
global journal of pure and applied sciences.
Language(s) - English
Resource type - Journals
ISSN - 1118-0579
DOI - 10.4314/gjpas.v27i1.5
Subject(s) - mathematics , operator (biology) , space (punctuation) , class (philosophy) , power (physics) , pure mathematics , operator theory , algebra over a field , physics , chemistry , computer science , quantum mechanics , biochemistry , repressor , artificial intelligence , transcription factor , gene , operating system
The concept of K-quasi-hyponormal operators on semi-Hilbertian space is defined by Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali in [7]. This paper is devoted to the study of new class of operators on semi-Hilbertian space H, ∥. ∥Acalled (n,m)power-A-quasi-hyponormal denoted [(n,m)QH]A.We give some basic properties of these operators and some examples are also given .An operator T ∈ BA(H) is said to be (n,m) power-A-quasi-hyponormal for some positive operator A and for some positive integers n and m if T⋕((T⋕)mTn— Tn(T⋕)m)T≥A or equivalently AT⋕((T⋕)mTn— Tn(T⋕)m)T≥0