Some results on the lattice of closed ideals of L^r(X) for X of the form (oplus_i l_p^i)_q

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Abstract

We study the lattice of closed (order and algebra) ideals of Lr(X) when X is a Banach lattice of the form (⨁iℓip)q (p∈[1,∞], q∈[1,∞)∪{0}&p≠q). We show that for every such X, Lr(X) has a unique maximal (order and algebra) ideal. For 1<p<∞ and q∈{0,1}, we show, in particular, that the lattice of closed (order and algebra) ideals of Lr(X) contains at least five distinct ideals.
Original languageEnglish
JournalStudia Mathematica
Early online date31 May 2021
DOIs
Publication statusEarly online date - 31 May 2021

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