Ball proximinality of M-ideals of compact operators

2020/08/15 by Jayanarayanan, C. R., Siju, Sreejith
#41A50 (Primary ) 47B07 #46B20 (secondary) #47A58 #47L05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2008.06769

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 K(ℓ₁), the space of compact operators on ℓ₁, is ball proximinal in B(ℓ₁), the space of bounded operators on ℓ₁, even though K(ℓ₁) is not an M-ideal in B(ℓ₁).

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