M-ideals of compact operators

Start: 5 December 2025 11:00
End: 5 December 2025 12:00
Categories: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario de Análisis Matemático, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: M-ideals of compact operators
By Manwook Han (Chungbuk National University, Republic of Korea)
Abstract: A closed subspace J of a Banach space X is called an M-ideal if and only if X^* = J^* \oplus_1 J^{\perp}. Note that if X = J \oplus_{\infty} J′, for some subspace J′ of X, then J is an M-ideal in X. However, the converse does not hold in general. Indeed, for real numbers p, q satisfying 1 < p ≤ q < ∞, the space K(\ell_p, \ell_q) of compact operators from \ell_p to \ell_q is an M-ideal in the space L(\ell_p, \ell_q) of bounded linear operators from \ell_p to \ell_q. On the other hand, L(\ell_p, \ell_q) cannot be represented as an \ell_{\infty}-sum of K(\ell_p, \ell_q) and any other subspace of L(\ell_p, \ell_q). In this talk, I will introduce several known properties that arise in such cases and present new results that connect this study to the theory of norm-attaining operators.