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Block matrix operators and weak hyponormalities. (English) Zbl 1197.47036

The authors introduce a new model of a block matrix operator \(M(\alpha,\beta)\) induced by two sequences \(\alpha\) and \(\beta\) and characterize its \(p\)-hyponormality. The model is viewed as arising from the composition operator \(C_T\) on \(\ell^2_+:=L^2(\mathbb N_0)\) induced by a measurable transformation \(T\) on the set of nonnegative integers \(\mathbb N_0\) with point mass measure. The authors use composition operator techniques to characterize the \(p\)-hyponormality of \(M(\alpha,\beta)\) and apply their results to obtain examples of these operators showing that the \(p\)-hyponormal classes are distinct. This paper will be useful for the bridge theory of Hilbert space operators.

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47B33 Linear composition operators
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