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August 7, 2024Proceedings of the American Mathematical SocietyOpen Access

Notes on a conjecture of Paszkiewicz on an ordered product of positive contractions

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Authors

HAHiroshi AndoUniversity of California, Irvine

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Implication

Theoretical analysis demonstrates strong operator topology convergence under two spectral conditions, indicating broader validity for positive contraction products.

Key Points

  • Strong operator topology convergence holds for Paszkiewicz’s conjecture whenever 1 is not in the essential spectrum or a faithful normal tracial state exists.
  • Theoretical analysis delivers an equivalent formulation of the conjecture and confirms that analogous weak convergence holds across separable hilbert spaces.
  • Highlights precise spectral conditions for infinite products of positive contractions, supporting broader progress on asymptotic operator convergence.

Cite This Study

Hiroshi Ando (2024) studied this question.

synapsesocial.com/papers/68e5d346b6db643587568f48https://doi.org/10.1090/proc/17028
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