Polynomial embeddings of unilateral weighted shifts in 2-variable weighted shifts (Q824390)

Given a unilateral weighted shift \(W_\omega\) with a bounded sequence \(\omega\) of positive numbers, the authors examine various ways in which the sequence \(\omega\) can give rise to a \(2\)-variable weight diagram, corresponding to a \(2\)-variable weighted shift. They introduce the so-called polynomial embeddings of unilateral weighted shifts in 2-variable weighted shifts and prove that every polynomial embedding of a subnormal unilateral weighted shift is subnormal. Then they answer certain natural questions, in particular, if certain specific unilateral weighted shifts can be embedded in a subnormal \(2\)-variable spherically isometric weighted shift.