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 language | English |
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Journal | Studia Mathematica |
Early online date | 31 May 2021 |
DOIs | |
Publication status | Early online date - 31 May 2021 |