The signless Laplacian matrix of a hypergraph H is defined to be \(\mathcal {Q}(H):=\mathcal {B}(H)\mathcal {B}(H)^T\) , where \(\mathcal {B}(H)\) is the (vertex-edge) incidence matrix of H. For a connected k-uniform hypergraph H with the maximum degree \(\Delta \) and average degree \(\bar{d}\) , Cardoso and Trevisan (2022) proved that \(k\bar{d}\le \rho (H)\le k\Delta \) with equality if and only if H is regular, where \(\rho (H)\) is the spectral radius of \(\mathcal {Q}(H)\) . In this paper, we refine this result for a connected irregular k-uniform hypergraph H by showing that \(\begin{aligned} \frac{k(\Delta -\delta )^2}{4n\Delta }+k\bar{d}< \rho (H)< k\Delta -\frac{\max \{k,4\}}{n(4D-1)}, \end{aligned}\) where D is the diameter of H and \(\delta \) is the minimum degree of vertices in H. Moreover, if \(D\ge k+1\) , the upper bound can further be improved as \(\begin{aligned} \rho (H)< k\Delta -\frac{2k}{n(4D-1)}. \end{aligned}\) Our results generalize some known results for connected irregular graphs.
