On $m$-partial isometries: spectra, weighted shifts, and similarity

The aim of this paper is to study $m$-partial isometries on Hilbert spaces, a natural extension of partial isometries and $m$-isometries. We establish structural and spectral results, characterize the $m$-partial isometric weighted shifts, and investigate similarity to $m$-isometries and $m$-partial isometries.