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arXiv · 2507.06511

$k$-quasi $n$-power posinormal Weighted Composition and Cauchy Dual of Moore-Penrose inverse of Lambert Operators

Sophiya S Dharan·T. Prasad·P. Ramya·M. H. M. Rashid
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Abstract

In this paper we characterize \(k\)-quasi \(n\)-power posinormal composition operators and weighted composition operators on the Hilbert space \(L^2(\Sigma)\). For Lambert conditional operators (of the form \(T = M_w E M_u\)), we establish necessary and sufficient conditions under which these Cauchy duals via the Moore-Penrose inverse become \(k\)-quasi \(n\)-power posinormal operators. Finally, we construct an explicit example of a \(k\)-quasi \(n\)-power posinormal weighted shift operator on a rooted directed tree.

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Sophiya S Dharan, T. Prasad, P. Ramya, M. H. M. Rashid. 2025-07-09. $k$-quasi $n$-power posinormal Weighted Composition and Cauchy Dual of Moore-Penrose inverse of Lambert Operators. https://arxiv.org/abs/2507.06511

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