2019/06/12 by Jablonski, Z. J., Jung, I. B., Stochel, J. · 2 citations
#47A75 #47B20 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1906.05215
In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an m-isometry for an unspecified m written in terms of conditions that are applied to "one vector at a time". We provide criteria for orthogonality of generalized eigenvectors of an (a priori unbounded) linear operator T on an inner product space that correspond to distinct eigenvalues of modulus 1. We also discuss a similar question of when Jordan blocks of T corresponding to distinct eigenvalues of modulus 1 are "orthogonal".