Biseparating linear maps between continuous vector-valued function spaces

Hwa Long Gau, Jyh Shyang Jeang, Ngai Ching Wong

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Let X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map T: C(X, E) → C(Y, F) is separating if Tf, Tg have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and T-1 are separating) is a weighted composition operator Tf = h · f ο φ Here, h is a function from Y into the set of invertible linear operators from E onto F, and φ is a homeomorphism from Y onto X. We also show that T is bounded if and only if h (y) is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect to the strong operator topology.

Original languageEnglish
Pages (from-to)101-109
Number of pages9
JournalJournal of the Australian Mathematical Society
Issue number1
StatePublished - Feb 2003


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