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Differences and Commutators of Projections on a Hilbert Space

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Abstract

We establish some new properties of pairs of idempotents and pairs of projections on a Hilbert space. The functional dependences of some operators associated with a pair of projections are found. Particular attention is paid to pairs of isoclinic projections. Such projections play an important role in non-commutative measure theory. Several relationships were obtained for the determinants. We also present an operator relation characterizing the non-trivial invariant subspace of such an operator.

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Acknowledgements

The work was performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2021-1393).

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  1. Leading Researcher, Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008, Russia

    Airat Bikchentaev

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  1. Airat Bikchentaev
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Correspondence to Airat Bikchentaev.

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Bikchentaev, A. Differences and Commutators of Projections on a Hilbert Space. Int J Theor Phys 61, 2 (2022). https://doi.org/10.1007/s10773-022-04973-7

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