Geodesic
A new complemented subspace for the Lorentz sequence spaces, with an application to its lattice of closed ideals
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 759-769

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DOI

We show that every Lorentz sequence space $d(\textbf {w},p)$ admits a 1-complemented subspace Y distinct from $\ell _p$ and containing no isomorph of $d(\textbf {w},p)$. In the general case, this is only the second nontrivial complemented subspace in $d(\textbf {w},p)$ yet known. We also give an explicit representation of Y in the special case $\textbf {w}=(n^{-\theta })_{n=1}^\infty $ ($0<\theta <1$) as the $\ell _p$-sum of finite-dimensional copies of $d(\textbf {w},p)$. As an application, we find a sixth distinct element in the lattice of closed ideals of $\mathcal {L}(d(\textbf {w},p))$, of which only five were previously known in the general case.
DOI : 10.4153/S0008439521000576
Mots-clés : Lorentz sequence spaces, complemented subspaces, lattice of closed ideals 
Wallis, Ben. A new complemented subspace for the Lorentz sequence spaces, with an application to its lattice of closed ideals. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 759-769. doi: 10.4153/S0008439521000576
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     title = {A new complemented subspace for the {Lorentz} sequence spaces, with an application to its lattice of closed ideals},
     journal = {Canadian mathematical bulletin},
     pages = {759--769},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000576},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000576/}
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