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Polar Decomposition and Functional Calculus for Generalized Tomita’s Observables

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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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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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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).

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