Isometries of combinatorial Banach spaces

2019/07/16 by Brech, C., Ferenczi, V., Tcaciuc, A. · 1 citation
#03E05 #03E75 #46B04 #46B45 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1907.06815

Abstract

We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are given by a change of signs of the elements of the basis. Our results hold for both the real and the complex cases.

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