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arXiv · 1901.00310

Which multiplication operators are surjective isometries?

Eugene Bilokopytov
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Abstract

Let $\mathbf{F}$ be a Banach space of continuous functions over a connected locally compact space $X$. We present several sufficient conditions on $\mathbf{F}$ guaranteeing that the only multiplication operators on $\mathbf{F}$ that are surjective isometries are scalar multiples of the identity. The conditions are given via the properties of the inclusion operator from $\mathbf{F}$ into $\mathcal{C}\left(X\right)$, as well as in terms of geometry of $\mathbf{F}$. An important tool in our investigation is the notion of Birkhoff Orthogonality.

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BibTeXRIS

Eugene Bilokopytov. 2019-01-02. Which multiplication operators are surjective isometries?. https://doi.org/10.1016/j.jmaa.2019.07.058

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