Monotone Relations in Hadamard Spaces

Ali Moslemipour; Mehdi Roohi

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arXiv · 1906.00396

Monotone Relations in Hadamard Spaces

Ali Moslemipour·Mehdi Roohi

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Abstract

In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^{\lozenge}$ is introduced and investigated, where $X$ is an Hadamard space and $X^{\lozenge}$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times X^{\lozenge}$ has $\mathcal{W}$-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with $\mathcal{W}$-property (and hence in flat Hadamard spaces) is proved.

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BibTeX RIS

Ali Moslemipour, Mehdi Roohi. 2019-06-02. Monotone Relations in Hadamard Spaces. https://arxiv.org/abs/1906.00396

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