## 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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