Strong ball proximinality of the space of compact operators
Volume 268 / 2023
Studia Mathematica 268 (2023), 51-64 MSC: Primary 46B20; Secondary 41A65, 46B28, 47B07. DOI: 10.4064/sm211009-29-5 Published online: 20 July 2022
We prove that the closed unit ball of the space of compact operators on a Hilbert space is strongly proximinal in the corresponding space of all bounded operators under an additional assumption. We also give a sufficient condition for an $M$-summand to be strongly ball proximinal. In addition, we prove that the space of bounded operators on a Hilbert space is strongly ball proximinal in itself under an additional assumption.