Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball

@inproceedings{Salomon2017AlgebrasOB,
  title={Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball},
  author={Guy Salomon and Orr Shalit and Eli Shamovich},
  year={2017}
}
We study algebras of bounded, noncommutative (nc) analytic functions on nc subvarieties of the nc unit ball. Given an nc variety V in the nc unit ball Bd, we identify the algebra of bounded analytic functions on V — denoted H∞(V) — as the multiplier algebra MultHV of a certain reproducing kernel Hilbert space HV consisting of nc functions on V. We find that every such algebra H∞(V) is completely isometrically isomorphic to the quotient H(Bd)/JV of the algebra of bounded nc holomorphic functions… CONTINUE READING

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