We create a new family of Banach spaces, the James–Schreier spaces, by amalgamating two important classical Banach spaces: James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. We then investigate the properties of these James–Schreier spaces, paying particular attention to how key properties of their ‘a...

Jim Valentine went to college on the GI Bill (a WWII veterans privilege) and has been there ever since; at present he is Professor of Integrative Biology, Emeritus, at UC Berkeley. His early research was on what is now called macroecology, working with fossil marine faunas, leading to a book, Evolutionary Paleoecology of the Marine Biosphere. Those studies continue today, chiefly with colleague...