Which multiplication operators are surjective isometries?

[摘要] Let F be a Banach space of continuous functions over a connected locally compact space X. We present several sufficient conditions on F guaranteeing that the only multiplication operators on F that are surjective isometrics are scalar multiples of the identity. The conditions are given via the properties of the inclusion operator from F into C (X), as well as in terms of geometry of F. An important tool in our investigation is the notion of Birkhoff Orthogonality. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Function spaces;Multiplication operators;Surjective isometrics;Birkhoff orthogonality;Nearly strictly convex spaces