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arXiv · 1711.01805

Homogeneous $2$-shifts

Somnath Hazra
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Abstract

The classification of homogeneous scalar weighted shifts is known. Recently, Kor\'{a}nyi obtained a large class of inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shifts. In this paper, we construct two distinct classes of examples not in the list of Kor\'{a}nyi. It is then shown that these new examples of irreducible homogeneous bi-lateral $2$-by-$2$ block shifts, together with the ones found earlier by Kor\'{a}nyi, account for every unitarily inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shift.

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Somnath Hazra. 2017-11-06. Homogeneous $2$-shifts. https://arxiv.org/abs/1711.01805

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