Spaceability of the set of continuous linear injections from \(\ell_p\) to \(\ell_p\) with nowhere continuous inverses (Q2811527)

Thanks to recent results of \textit{S. Creswell}, see, e.g., [Missouri J. Math. Sci. 25, No. 2, 213--214 (2013; Zbl 1294.46021)], we know that such a kind of ``animals'', as the title describes, exist.NEWLINENEWLINECreswell first proved that they exist without demanding linearity, and then in the above mentioned paper also proved the existence of linear such ones. One may observe, as the authors do, that Creswell's examples work for any \(1<p<\infty\).NEWLINENEWLINEThe point of the paper under review is, in short, to demonstrate that not just do the animals exist, the set of such animals even contains a Banach space (it is spaceable) when placed in some natural universe (depending on whether one assumes linearity, and where one considers the operators to be defined)!NEWLINENEWLINEReviewer's remark: A big, new source for lineability and spaceability is the book [\textit{R. M. Aron} et al., Lineability. The search for linearity in mathematics. Boca Raton, FL: CRC Press (2016; Zbl 1348.46001)].