Abstract:We observe that the notion of an almost $\mathfrak{FI}_K$-universal based Banach space, introduced in our earlier paper [1]: Banakh T., Garbuli\'nska--W\c egrzyn J., {\it The universal Banach space with a $K$-suppression unconditional basis}, Comment. Math. Univ. Carolin. {\bf 59} (2018), no. 2, 195--206, is vacuous for $K=1$. Taking into account this discovery, we reformulate Theorem 5.2 from [1] in order to guarantee that the main results of [1] remain valid.
Keywords: 1-suppression unconditional Schauder basis; rational spaces; isometry
DOI: DOI 10.14712/1213-7243.2020.012
AMS Subject Classification: 46B04 46M15 46M40