Ball proximinality of $M$-ideals of compact operators

C. R. Jayanarayanan; Sreejith Siju

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arXiv · 2008.06769

Ball proximinality of $M$-ideals of compact operators

C. R. Jayanarayanan·Sreejith Siju

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Abstract

In this article, we prove the proximinality of closed unit ball of $M$-ideals of compact operators. We also prove the ball proximinality of $M$-embedded spaces in their biduals. Moreover, we show that $\mathcal{K}(\ell_1)$, the space of compact operators on $\ell_1$, is ball proximinal in $\mathcal{B}(\ell_1)$, the space of bounded operators on $\ell_1$, even though $\mathcal{K}(\ell_1)$ is not an $M$-ideal in $\mathcal{B}(\ell_1)$.

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BibTeX RIS

C. R. Jayanarayanan, Sreejith Siju. 2020-08-15. Ball proximinality of $M$-ideals of compact operators. https://arxiv.org/abs/2008.06769

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