An image problem for compact operators

Chalendar, Isabelle; Partington, Jonathan

doi:10.1090/S0002-9939-05-08084-6

An image problem for compact operators
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by Isabelle Chalendar and Jonathan R. Partington PDF

Proc. Amer. Math. Soc. 134 (2006), 1391-1396 Request permission

Abstract:

Let $\mathcal {X}$ be a separable Banach space and $(\mathcal {X}_n)_n$ a sequence of closed subspaces of $\mathcal {X}$ satisfying $\mathcal {X}_n\subset \mathcal {X}_{n+1}$ for all $n$. We first prove the existence of a dense-range and injective compact operator $K$ such that each $K\mathcal {X}_n$ is a dense subset of $\mathcal {X}_n$, solving a problem of Yahaghi (2004). Our second main result concerns isomorphic and dense-range injective compact mappings between dense sets of linearly independent vectors, extending a result of Grivaux (2003).

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