Irreducible Tuples Without the Boundary Property. Issue 1 (1st March 2015) - Chavan, Sameer
Abstract: We examine spectral behavior of irreducible tuples that do not admit the boundary property. In particular, we prove under some mild assumption that the spectral radius of such an m -tuple ( T_1, . . . , T_m ) must be the operator norm of T_1^* T_1 + . . . + T_m^*T_m . We use this simple observation to ensure the boundary property for an irreducible, essentially normal, joint q-isometry, provided it is not a joint isometry. We further exhibit a family of reproducing Hilbert C[ z_1, . . . , z_m ] -modules (of which the Drury–Arveson Hilbert module is a prototype) with the property that any two nested unitarily equivalent submodules are indeed equal.