Monotone Relations in Hadamard Spaces

Ali Moslemipour, Mehdi Roohi, Mohammad Reza Mardanbeigi, Mahdi Azhini


In this paper,  the notion of $\mathcal{W}$-property for subsets of $X\times X^\loze$ is introduced  and investigated, where $X$ is an Hadamard space and $X^\loze$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times X^\loze$ 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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