OnWeighted Adjacency Operators Associated to Directed Graphs

George Exner, Il Bong Jung, Eun Young Lee, Minjung Seo


The weighted adjacency operators associated to directed graphs are defined and some operator properties such as normality and
hyponormality are investigated. As well, the weighted adjacency operators associated to a forested circuit are defined and their fundamental operator properties are studied. We produce some examples showing the properties of $p$-hyponormality and $p$
-paranormality are distinct for $p\in (0,\infty ).$ Basic connections between directed graphs and Hilbert space operators are discussed.

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