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

Benali Abdelkader

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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References


M.L. Arias, G. Corach, M.C. Gonzalez, Partial isometries in semi-

Hilbertian spaces, Linear Algebra Appl, 428, (7), (2008), 1460-1475.

DOI:10.1016/j.laa.2007.09.031.

M.L. Arias, G. Corach, M.C. Gonzalez, Metric properties of projections in semi-

Hilbertian spaces, Integral Equations Operator Theory , 62 (1),(2008).11-28

Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali, Hyponor-

mal And k-Quasi-hyponormal Operators On Semi-Hilbertian Spaces, The

Australian Journal of Mathematical Analysis and Applications (2016).

doi:10.1155/2012/975745.

A.Aluthge, On p-hyponormal Operators for 0 ≺ p ≺ 1, Integral Equations

Operators Theory , 13( 1990), 307-315.

Cherifa Chelalli and Abdelkader Benali , Class of (A, n)-power-Hyponormal

and Quasihyponormal operators in semi-hilbertian space, Functional Analysis

Approximation And Computation 11(2)(2019), 13-21.

B. P. DUGGAL,Tensor products of operators-strong stability and p-

hyponormality, Glasgow Math journal,42(2000),pp 371-381

M. C. GONZALEZ, Operator norm inequalities in semi-Hilbertian spaces, Lin-

ear Algebra and its Applications, 434 (2011), pp. 370-378.

Samir Al Mohammady, Sid Ahmed Ould Beinane and Ould Ahmed Mahmoud

Sid Ahmed, On(n, m)-A-power-normal and (n, m)-A-power quasi-normal op-

erators in semi-hilbertian space,Mathematica Bohemica (February 2020)

O. A. MAHMOUD SID AHMED and A. SADDI, A-m-Isomertic operators in

semi-Hilbertian spaces, Linear Algebra and its Applications, 436 (2012), pp.

-3942.

Messaoud Guesba and Mostefa Nadir On n-power-hyponormal operators

Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume

, Number 1 (2016), pp. 473-479

A. SADDI, A- Normal operators in Semi-Hilbertian spaces, The Australian

Journal of Mathematical Analysis and Applications Volume 9,issue 1,Article

,(2012),pp 1-12


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