Kazan (Volga region) Federal University, KFU
Form of presentationArticles in international journals and collections
Year of publication2021
  • Bikchentaev Ayrat Midkhatovich, author
  • Bibliographic description in the original language A. M. Bikchentaev, Trace inequalities for Rickart $C^*$-algebras // Positivity 25 (2021), no. 5, 1943--1957.
    Annotation Rickart $C^*$-algebras are unital and satisfy polar decomposition. We proved that if a unital $C^*$-algebra $\mathcal{A}$ satisfies polar decomposition and admits ``good'' faithful tracial states then $\mathcal{A}$ is a Rickart $C^*$-algebra. Via polar decomposition we characteri\-zed tracial states among all states on a Rickart $C^*$-algebra. We presented the triangle inequality for Hermitian elements and traces on Rickart $C^*$-algebra. For a block projection operator and a trace on a Rickart $C^*$-algebra we proved a new inequality. As a corollary, we obtain a sharp estimate for a trace of the commutator of any Hermitian element and a projection. Also we give a characterization of traces in a wide class of weights on a von Neumann algebra.
    Keywords Hilbert space, polar decomposition, von Neumann algebra, $C^*$-algebra, weight, trace
    The name of the journal POSITIVITY
    URL https://doi.org/10.1007/s11117-021-00852-3
    Please use this ID to quote from or refer to the card https://repository.kpfu.ru/eng/?p_id=255300&p_lang=2
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