Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 18 (2023), 13 -- 26

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This work is licensed under a Creative Commons Attribution 4.0 International License.

SOME RESULTS ON C-NORMAL OPERATORS

Ismail Lakehal and Messaoud Guesba

Abstract. A bounded linear operator on a complex Hilbert space ℋ is a C-normal operator if there exists a conjugation C on ℋ such that CT* TC=TT* . This class of operators seems a natural generalization of C-symmetric operators on a Hilbert space. In this paper, several results related to such a family are established. Then, we give sufficient conditions under which the product and sum of two C-normal operators is C-normal. Moreover, we investigate properties of tensor products of these operators. Some more associated for this class of operators are obtained.

2020 Mathematics Subject Classification: 47A05; 47A55; 47B15
Keywords: C -symmetric; C-skew-symmetric; C-normal; conjugation.

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Ismail Lakehal
Faculty of Exact Sciences, Department of Mathematics
El Oued University, 39000 Algeria
e-mail: ismaillakehal28@gmail.com

Messaoud Guesba
Faculty of Exact Sciences, Department of Mathematics
El Oued University, 39000 Algeria.
e-mail: guesbamessaoud2@gmail.com,
guesba-messaoud@univ-eloued.dz

http://www.utgjiu.ro/math/sma