Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

F. Berezin and L. Faddeev have interpreted the Fermi zero-range model as a self-adjoint extension of the Laplacian. Various modifications of this model possess rich spectral properties, but unavoidably have negative effective radius and contain numerous parameters which do not have a direct physical meaning. We suggest, for spherically-symmetric scattering, a generalization of the Fermi zero-ra...

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

In 1990, Cvetkovi? and Rowlinson conjectured that among all outerplanar graphs on n vertices, K 1 ? P ? attains the maximum spectral radius. 2017, Tait Tobin confirmed conjecture for sufficientlty large values of n. this article, we show is true ? 2 except = 6.

We present an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.