Isomorphisms of spaces of affine continuous complex functions

  • Jakub Rondoš
  • Jiří Spurný

Abstract

Let $X$ and $Y$ be compact convex sets such that their each extreme point is a weak peak point. We show that $\operatorname{ext} X$ is homeomorphic to $\operatorname{ext} Y$ provided there exists a small-bound isomorphism of the space $\mathfrak{A}(X,\mathbb{C} )$ of continuous affine complex functions on $X$ onto $\mathfrak{A}(Y,\mathbb{C} )$. Further, we generalize a result of Cengiz to the context of compact convex sets.

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Published
2019-10-19
How to Cite
Rondoš, J., & Spurný, J. (2019). Isomorphisms of spaces of affine continuous complex functions. MATHEMATICA SCANDINAVICA, 125(2), 270-290. https://doi.org/10.7146/math.scand.a-114989
Section
Articles