Guirao, Antonio J.; Montesinos, Vicente; Zizler, Václav Open problems in the geometry and analysis of Banach spaces. (English) Zbl 1351.46001 Cham: Springer (ISBN 978-3-319-33571-1/hbk; 978-3-319-33572-8/ebook). xii, 169 p. (2016). In every field of mathematics there are monographs describing the present knowledge in that area. It is likewise important to have compendia telling us what we do not yet know; the book under review does exactly this for the theory of Banach spaces.The authors have selected 304 open problems (actually, it seems that one or two have already been solved); for each of them they present information on partial solutions and pointers to the literature. The problems are grouped into seven chapters (Basic Linear Structure; Basic Linear Geometry; Biorthogonal Systems; Differentiability and Structure, Renormings; Nonlinear Geometry; Some More Nonseparable Problems; Some Applications) and they range from deep classical problems such as the separable quotient problem (Does every Banach space admit a separable quotient space?)to rather concrete questions that still have defied all attempts to answer them, e.g., Does every \(2\)-dimensional Hilbert space have Lindenstrauss’s Property (B)?At the end of the book there are an extended and very useful subject index and an alphabetical list of concepts and problems that help the reader to locate problems involving a particular topic.This collection will be attractive to researchers in Banach space theory and to prospective PhD students in this field. Reviewer: Dirk Werner (Berlin) Cited in 4 ReviewsCited in 26 Documents MSC: 46-02 Research exposition (monographs, survey articles) pertaining to functional analysis 00A27 Lists of open problems 46B03 Isomorphic theory (including renorming) of Banach spaces 46B04 Isometric theory of Banach spaces 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces 46B20 Geometry and structure of normed linear spaces 46B26 Nonseparable Banach spaces 46B80 Nonlinear classification of Banach spaces; nonlinear quotients Keywords:Banach space theory; open problems PDFBibTeX XMLCite \textit{A. J. Guirao} et al., Open problems in the geometry and analysis of Banach spaces. Cham: Springer (2016; Zbl 1351.46001) Full Text: DOI