A short note on the similarity of operator-valued multishifts. (English) Zbl 07921913
Summary: A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of two (multi)shifts. Further, we utilize the aforementioned similarity criteria to determine the similarity between two tuples of operators of multiplication by the coordinate functions on certain reproducing kernel Hilbert spaces determined by diagonal kernels.
MSC:
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 46E40 | Spaces of vector- and operator-valued functions |
| 47B32 | Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) |
Keywords:
operator-valued multishift; similarity; unitary equivalence; vector-valued reproducing kernel Hilbert spacesReferences:
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