On the class of (n, m) power-A-hyponormal operators in semi-Hilbertian space

Djilali Bekai, Abdelkader Benali, Hakem Ali

Abstract


The concept of n-power-hyponormal operator on Hilbert space dended by
Messoud Guesba and Motafa Nadir in [10] and in [5] Cherifa Chellali and Ab-
delkader Benali they gave the other class ,class of (A, n)-power-hyponormal op-
erator in semi-hilbertien space.In this manuscript we introduce new class of op-
erators on semi-Helbertian space (H, k.kA) called (n, m) power-A-hyponormal
denoted [(n, m)H]A
.We study some basic properties of these operators and
some examples are also given .An operator T ∈ BA(H) is (n, m) power-A-
hyponormal for some positive operator A and for some positive integers n and
m if (T
]
)
mT
n − T
n
(T
]
)
m ≥A 0.


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