• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.711-732
• /
• 2018

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.

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.225-251
• /
• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.