Journal of Scientific Research and Reports

n-Normal and n-Quasi-normal Composite Multiplication Operator on L2 -Spaces

S. Senthil

Department of Mathematics, Vickram College of Engineering, Enathi, Tamilnadu, India.

P. Thangaraju *

Department of Mathematics, Saraswathi Narayanan College, Madurai, Tamilnadu, India.

D. C. Kumar

Department of Mathematics, Vickram College of Engineering, Enathi, Tamilnadu, India.

*Author to whom correspondence should be addressed.

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Abstract

An operator A is called n-normal operator if AⁿA^* =A^*Aⁿ and n-quasi-normal operator if AⁿA^*A =A^*AAⁿ . In this paper we characterize the essential isometry, essential co-isometry n-normal and n-quasi-normal composite multiplication operator on L² -Spaces under certain conditions.

Keywords: Essential isometry, essential co-isometry, n-normal, n-quasi-normal, conditional expectation, composition operator, multiplication operator and composite multiplication operator.

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