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- W2338886987 abstract "We extend some of the results of Agler, Knese, and McCarthy [1] to $n$-tuples of commuting isometries for $n>2$. Let $mathbb{V}=(V_1,dots,V_n)$ be an $n$-tuple of a commuting isometries on a Hilbert space and let Ann$(mathbb{V})$ denote the set of all $n$-variable polynomials $p$ such that $p(mathbb{V})=0$. When Ann$(mathbb{V})$ defines an affine algebraic variety of dimension 1 and $mathbb{V}$ is completely non-unitary, we show that $mathbb{V}$ decomposes as a direct sum of $n$-tuples $mathbb{W}=(W_1,dots,W_n)$ with the property that, for each $i=1,dots,n$, $W_i$ is either a shift or a scalar multiple of the identity. If $mathbb{V}$ is a cyclic $n$-tuple of commuting shifts, then we show that $mathbb{V}$ is determined by Ann$(mathbb{V})$ up to near unitary equivalence, as defined in [1]." @default.
- W2338886987 created "2016-06-24" @default.
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- W2338886987 date "2016-04-21" @default.
- W2338886987 modified "2023-09-27" @default.
- W2338886987 title "On polynomial $n$-tuples of commuting isometries" @default.
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