Trimming the Johnson bonsai
F\'elix Cabello S\'anchez, Jes\'us M. F. Castillo, Yolanda Moreno

TL;DR
This paper investigates the structure of subspaces of l_p(\u03b3) for various p, showing they are sums of separable subspaces when p>1, and provides examples of more complex subspaces for 0<pnd discusses properties like SCP and SEP.
Contribution
It establishes the structure of subspaces of l_p(3) for p>1 and constructs examples for 0<pemonstrating more intricate subspace behavior, linking to properties like SCP and SEP.
Findings
Subspaces of l_p(3) are l_p-sums for p>1.
Existence of non-l_p-sum subspaces for 0<pemonstrated.
Kernel of quotient maps relate to properties like SCP and SEP.
Abstract
We show that if every subspace of is an -sum of separable subspaces of , and we provide examples of subspaces of for that are not even isomorphic to any -sum of separable spaces, notably the kernel of any quotient map with uncountable. We involve the separable complementation property (SCP) and the separable extension property (SEP), showing that if is a Banach space of density character with the SCP then the kernel of any quotient map is a complemented subspace of a space with the SCP and, consequently, has the SEP.
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Taxonomy
TopicsUrban and spatial planning
