A new complemented subspace for the Lorentz sequence spaces, with an application to its lattice of closed ideals

2020/12/16 by Wallis, Ben
#46B20 #46B45 #47L20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.08935

Abstract

We show that every Lorentz sequence space d(w,p) admits a 1-complemented subspace Y distinct from ℓ_p and containing no isomorph of d(w,p). In the general case, this is only the second nontrivial complemented subspace in d(w,p) yet known. We also give an explicit representation of Y in the special case w=(n^-θ)_n=1^∞ (0

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