Kazan (Volga region) Federal University, KFU
Form of presentationArticles in international journals and collections
Year of publication2019
  • Bikchentaev Ayrat Midkhatovich, author
  • Bibliographic description in the original language A.M. Bikchentaev, Ideal $F$-norms on $C^*$-algebras. II // Russian Mathematics, 2019, Vol. 63, No. 3. P. 78-82.
    Annotation We study ideal $F$-norms $\|\cdot\|_p$, $0 < p <+\infty$ associated with a trace $\varphi$ on a $C^*$-algebra $\mathcal{A}$. If $A, B$ of $\mathcal{A}$ are such that $|A|\leq |B|$, then $\|A\|_p \leq \|B\|_p$. We have $\|A\|_p=\|A^*\|_p$ for all $A$ from $\mathcal{A}$ ($0 < p <+\infty$) and a seminorm $\|\cdot\|_p$ for $1 \leq p <+\infty$. We estimate the distance from any element of a unital $\mathcal{A}$ to the scalar subalgebra in the seminorm $\|\cdot\|_1$. We investigate geometric properties of semiorthogonal projections from $\mathcal{A}$. If a trace $\varphi$ is finite, then the set of all finite sums of pairwise products of projections and semiorthogonal projections (in any order) of $\mathcal{A}$ with coefficients from $\mathbb{R}^+ $ is not dense in $\mathcal{A}$.
    Keywords Hilbert space, linear operator, projection, semiorthogonal projection, unitary operator, inequality, $C^*$-algebra, trace, ideal $F$-norm.
    The name of the journal Russian Mathematics
    Please use this ID to quote from or refer to the card https://repository.kpfu.ru/eng/?p_id=198020&p_lang=2

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