NONCOMMUTATIVE HYPERBOLIC GEOMETRY ON THE UNIT BALL OF B(H) n

@inproceedings{Xnx2008NONCOMMUTATIVEHG,
  title={NONCOMMUTATIVE HYPERBOLIC GEOMETRY ON THE UNIT BALL OF B(H) n},
  author={Xnx and M Rn},
  year={2008}
}
  • Xnx, M Rn
  • Published 2008
In this paper we introduce a hyperbolic (Poincaré-Bergman type) distance δ on the non-commutative open ball where B(H) is the algebra of all bounded linear operators on a Hilbert space H. It is proved that δ is invariant under the action of the free holomorphic automorphism group of [B(H) n ] for all Ψ ∈ Aut([B(H) n ] 1). Moreover, we show that the δ-topology and the usual operator norm topology coincide on [B(H) n ] 1. While the open ball [B(H) n ] 1 is not a complete metric space with respect… CONTINUE READING

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