Characterizations of Hopfians spaces

Abstract

. A Banach space X is called Hop fi an, if any bounded linear operator surjective is bijective. The existence of the Banach Hop fi ans spaces in in fi nite dimension was established by Gowers and Maury in 1993. In this note we obtain some characterizations of Banach spaces Hop fi ans by properties of the algebra of bounded linear operators B ( X ) . Mathematics subject classi fi cation (2020): 47A10, 47A11.