On the tameness of power series space pairs

Year 2026, Volume: 55 Issue: 2 , 555 - 566 , 29.04.2026

Buket Can Bahadir

https://doi.org/10.15672/hujms.1717066

https://izlik.org/JA49ZZ95DD

Abstract

In this paper, it is shown that the tameness of the Köthe space pair $(\lambda^p(A),\lambda^q(B))$ is determined solely by the tameness of the family of quasi-diagonal operators defined between the pair of spaces. We use this tool to fill the gaps in characterization of pairs of power series spaces, adding to the previously established results of Dubinsky, Vogt [Stud. Math. \textbf{93}, 71-85 1989], Nyberg [Trans. Amer. Math. Soc. \textbf{283}, 645-660, 1984] and others, and summarize this complete characterization in Table 1. As a result, we also show that the range of every continuous tame operator defined between power series spaces of infinite type has a basis.

Keywords

Fréchet space , Köthe space , Tame operator

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