Unboundedness of adjacency matrices of locally finite graphs

Details Unboundedness of adjacency matrices of locally finite graphs Unboundedness of adjacency matrices of locally finite graphs

2009-10-19

arxiv.org/abs/0910.3466v3

Mathematics

Functional Analysis

Typos corrected. Examples added. Cute drawings. Simplification of the main condition. Case of the weight tending to zero more

Scientific paper

Given a locally finite simple graph so that its degree is not bounded, every
self-adjoint realization of the adjacency matrix is unbounded from above. In
this note we give an optimal condition to ensure it is also unbounded from
below. We also consider the case of weighted graphs. We discuss the question of
self-adjoint extensions and prove an optimal criterium.

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