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Homogeneous 2-Shifts

  • Somnath Hazra
Article
  • 8 Downloads

Abstract

The classification of homogeneous scalar weighted shifts is known. Recently, Korányi 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 Korányi. 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 Korányi, account for every unitarily inequivalent irreducible homogeneous bi-lateral 2-by-2 block shift.

Keywords

Homogeneous operators Projective representations Associated representation 

Mathematics Subject Classification

Primary 47B37 Secondary 20C25 

Notes

Acknowledgements

The author would like to express his sincere gratitude to G. Misra for his patient guidance and suggestions in the preparation of this paper. The author is grateful to the referee for many useful comments and suggestions. The author would like to thank Professor Adam Korányi for many important comments.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institutte of ScienceBangaloreIndia

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