A Cyclic Subnormal Completion of Complex Data

• Journal title : Kyungpook mathematical journal
• Volume 54, Issue 2,  2014, pp.157-163
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2014.54.2.157
Title & Authors
A Cyclic Subnormal Completion of Complex Data
Jung, Il Bong; Li, Chunji; Park, Sun Hyun;

Abstract
For a finite subset $\small{{\Lambda}}$ of $\small{\mathbb{N}_0{\times}\mathbb{N}_0}$, where $\small{\mathbb{N}_0}$ is the set of nonnegative integers, we say that a complex data $\small{{\gamma}_{\Lambda}:=\{{\gamma}_{ij}\}_{(ij){\in}{\Lambda}}}$ in the unit disc $\small{\mathbf{D}}$ of complex numbers has a cyclic subnormal completion if there exists a Hilbert space $\small{\mathcal{H}}$ and a cyclic subnormal operator S on $\small{\mathcal{H}}$ with a unit cyclic vector $\small{x_0{\in}\mathcal{H}}$ such that $\small{{\langle}S^{*i}S^jx_0,x_0{\rangle}={\gamma}_{ij}}$ for all $\small{i,j{\in}\mathbb{N}_0}$. In this note, we obtain some sufficient conditions for a cyclic subnormal completion of $\small{{\gamma}_{\Lambda}}$, where $\small{{\Lambda}}$ is a finite subset of $\small{\mathbb{N}_0{\times}\mathbb{N}_0}$.
Keywords
subnormal completion;cyclic vector;truncated moment matrix;flat extension;
Language
English
Cited by
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