## Contributed talks session A (Monday)

#### Event Title

On polynomial n-tuples of commuting isometries

#### Location

Cupples I Room 207

#### Start Date

7-18-2016 4:00 PM

#### End Date

18-7-2016 4:20 PM

#### Description

We extend some of the results of Agler, Knese, and McCarthy concerning pairs of commuting shifts to the case of n-tuples of commuting isometries, where n>2. Let \$V=(V_1,\dots,V_n)\$ be an \$n\$-tuple of commuting isometries on a Hilbert space and let Ann(\$V\$) denote the set of all \$n\$-variable polynomials \$p\$ such that \$p(V)=0\$. When Ann(\$V\$) defines an affine algebraic variety of dimension 1 and \$V\$ is completely non-unitary, we show that \$V\$ decomposes as a direct of \$n\$-tuples \$(W_1,\dots,W_n)\$ with the property that, for each \$i\$, \$W_i\$ is either a shift or a scalar multiple of the identity. If \$V\$ is a cyclic \$n\$-tuple of commuting shifts, then we show that \$V\$ is determined by Ann(\$V\$) up to near unitary equivalence.

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COinS

Jul 18th, 4:00 PM Jul 18th, 4:20 PM

On polynomial n-tuples of commuting isometries

Cupples I Room 207

We extend some of the results of Agler, Knese, and McCarthy concerning pairs of commuting shifts to the case of n-tuples of commuting isometries, where n>2. Let \$V=(V_1,\dots,V_n)\$ be an \$n\$-tuple of commuting isometries on a Hilbert space and let Ann(\$V\$) denote the set of all \$n\$-variable polynomials \$p\$ such that \$p(V)=0\$. When Ann(\$V\$) defines an affine algebraic variety of dimension 1 and \$V\$ is completely non-unitary, we show that \$V\$ decomposes as a direct of \$n\$-tuples \$(W_1,\dots,W_n)\$ with the property that, for each \$i\$, \$W_i\$ is either a shift or a scalar multiple of the identity. If \$V\$ is a cyclic \$n\$-tuple of commuting shifts, then we show that \$V\$ is determined by Ann(\$V\$) up to near unitary equivalence.