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Drazin inverse of Lambert conditional type operators

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Abstract

In this paper, We prove some results for Drazin inverse of Lambert conditional operators, denoted by \(T^d\), on \(L^2(\Sigma )\). Also we introduce some new classes of operators and we give some necessary and sufficient conditions for \(T^d\) to belong in these classes. In addition, polar decomposition, Aluthge transform and complex symmetry of \(T^d\) will be investigated. Moreover, we establish lower and upper bounds for the numerical radius of \(T^d\). Finally, by using the matrix representation, some practical examples are provided to illustrate the obtained results.

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  1. Department of Mathematics, Lorestan University, Khorramabad, Iran

    M. Sohrabi

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  1. M. Sohrabi
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Correspondence to M. Sohrabi.

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Sohrabi, M. Drazin inverse of Lambert conditional type operators. Rend. Circ. Mat. Palermo, II. Ser 72, 605–619 (2023). https://doi.org/10.1007/s12215-021-00693-9

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