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Polar Decomposition and Functional Calculus for Generalized Tomita’s Observables

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Abstract

Continuing previous studies by one of us (HI), a polar decomposition and a functional calculus for an unbounded Tomita’s observable are studied. For both problems we distinguish two different cases dictated by commutation properties.

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References

  1. Inoue, A.: Tomita’s Lectures on Observable Algebras in Hilbert Space, Lecture Notes in Mathematics 2285, Springer (2021)

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Acknowledgements

This work has been partially done within the activities of Gruppo UMI Teoria dell’Approssimazione e Applicazioni and of GNAMPA of the INdAM. One of us (H.I.) is supported by JSPS KAKENHI Grant Number 20K14335 and also acknoledges the financial support of CORI-Università di Palermo and the Kyushu Sangyo University.

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Authors and Affiliations

  1. Department of Economics, Kyushu Sangyo University, Fukuoka, Japan

    Hiroshi Inoue

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi n. 34, 90123, Palermo, Italy

    Camillo Trapani

Authors
  1. Hiroshi Inoue
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  2. Camillo Trapani
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The corresponding author attested to the conceptual and theoretical aspects of this paper. The co-authors gave the overall consistency of this paper and any physical or mathematical examples.

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Correspondence to Hiroshi Inoue.

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Communicated by Palle Jorgensen.

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Inoue, H., Trapani, C. Polar Decomposition and Functional Calculus for Generalized Tomita’s Observables. Complex Anal. Oper. Theory 18, 9 (2024). https://doi.org/10.1007/s11785-023-01449-2

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  • DOI: https://doi.org/10.1007/s11785-023-01449-2

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