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- W2953290400 abstract "A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ |T_1xi_1+T_2xi_2+... +T_dxi_d|^2leq |xi_1|^2+|xi_2|^2+...+|xi_d|^2 $ for all $xi_1,xi_2,...,xi_din H$. These are the higher dimensional counterparts of contractions. We show that many of the operator-theoretic aspects of function theory in the unit disk generalize to the unit ball B_d in complex d-space, including von Neumann's inequality and the model theory of contractions. These results depend on properties of the d-shift, a distinguished d-contraction which acts on a new $H^2$ space associated with B_d, and which is the higher dimensional counterpart of the unilateral shift. $H^2$ and the d-shift are highly unique. Indeed, by exploiting the noncommutative Choquet boundary of the d-shift relative to its generated C^*-algebra we find that there is more uniqueness in dimension $dgeq 2$ than there is in dimension one." @default.
- W2953290400 created "2019-06-27" @default.
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- W2953290400 date "1997-05-28" @default.
- W2953290400 modified "2023-09-27" @default.
- W2953290400 title "Subalgebras of C*-algebras III: multivariable operator theory" @default.
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