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The Joint Spectrum for a Commuting Pair of Isometries in Certain Cases

In: Multivariable Operator Theory

Author

Listed:
  • Tirthankar Bhattacharyya

    (Indian Institute of Science, Department of Mathematics)

  • Shubham Rastogi

    (Indian Institute of Science, Department of Mathematics)

  • U. Vijaya Kumar

    (Indian Institute of Science, Department of Mathematics)

Abstract

We show that the joint spectrum of two commuting isometries can vary widely depending on various factors. It can range from being small (of measure zero or an analytic disc for example) to the full bidisc. En route, we discover a new model pair in the negative defect case and relate it to the modified bi-shift.

Suggested Citation

  • Tirthankar Bhattacharyya & Shubham Rastogi & U. Vijaya Kumar, 2023. "The Joint Spectrum for a Commuting Pair of Isometries in Certain Cases," Springer Books, in: Ernst Albrecht & Raúl Curto & Michael Hartz & Mihai Putinar (ed.), Multivariable Operator Theory, pages 155-193, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50535-5_7
    DOI: 10.1007/978-3-031-50535-5_7
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