Some Properties of Binormal Operators

Hadeel Ali Hassan

Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University.

In this paper we have introduced some classes of operators like class of normal
operators and n-binormal operators and n-isometry operators on an infinite Hilbert
space H. We have given some basic properties of these classes of operators. In
general, every normal operator is not necessarily an isometry operator and we studied
the relationship between normal with n-isometry and normal with n-binormal .We
concluded the relationship between n-isometry with n-binormal.

Key Words: Normal operator , n-Normal operator, Binormal operator .


1. Al-Mosawi. R. R. and Hassan. H.H."A Note On Normal and n-Normal Operators". Journal of Thi-qar
2. Alzuraiqi, S. A. and Patel, A. B. "On normal operators". General Mathematical Notes, Vol. 1, No. 2, pp:61-73.
3. Gheondea, A. "When are the products of normal operators normal?", Bull. Math. Soc. Sci. Math. Roumanie
Tome . Vol. 52(100), No. 2, pp:129–150. (2009).
4. Jibril, A.A.S. "On n-power normal operators". The Arabian Journal of Science and Engineering, Vol. 33, No.
2A, pp:247-251. (2008).
5. Jibril, A.A.S. "On operators for which T∗2T2 = (T∗T)2". International Mathematical Forum, Vol. 5, No. 46,pp:2255-2262. (2010).
6. Panayappan, S. and Sivamani, N. "On n-binormal operators". General Mathematical Notes. Vol. 10, No. 2,
pp:1-8. (2012).
7. Panayappan, S. "On n-power class (Q) operators". International Journal of Mathematical Analysis, Vol. 6, No.
31, pp:1513-1518. (2012).