Some problems in functional analysis inspired by Hahn-Banach type theorems
This interesting survey paper deals with various aspects of the Hahn-Banach extension theorem for Banach spaces. Among the topics covered by the author are the following: applications of the Hahn-Banach theorem in analysis, Hahn-Banach type theorems for operators, uniqueness of the Hahn-Banach extension, the Hahn-Banach theorem for bilinear mappings, properties around the Hahn-Banach theorem characterising finite-dimensional spaces, characterisations of Hilbert spaces by Hahn-Banach type properties, intersection properties of balls, extension of Lipschitz maps. The author displays only few proofs, but points to the literature instead; the reference list, which contains a number of not so well-known papers, gives ample opportunity to pursue the subject matter further. The paper would have benefitted from proper proof-reading and copy-editing; there are mathematical ambiguities, language slips, misspelt names and typographical imperfections that could have been avoided.
scientific article; zbMATH DE number 6335713