Multivariable recursively generated weighted shifts and the 2-variable subnormal completion problem. (English) Zbl 07083935
Summary: In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide “concrete” necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.
MSC:
| 47B20 | Subnormal operators, hyponormal operators, etc. |
| 40A25 | Approximation to limiting values (summation of series, etc.) |
| 44A60 | Moment problems |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 47A20 | Dilations, extensions, compressions of linear operators |
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
Keywords:
subnormal completion problem; multivariable weighted shift; generalized Fibonacci sequence; moment problems; propagation phenomenaReferences:
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