Spectral domains in several complex variables

Siqi Fu, Bernard Russo

Research output: Contribution to journalArticlepeer-review


In this paper we study the concepts of spectral domain and complete spectral domain in several complex variables. For a domain Ω in Cn and an n-tuple T of commuting operators on a Hilbert space H such that the Taylor spectrum of T is a subset of Ω, we introduce the quantities KΩ(T) and MΩ(T). These quantities are related to the quantities KX(T) and MX(T) introduced by Paulsen for a compact subset X. When T is an n-tuple of 2×2 matrices, KΩ(T) and MΩ(T) are expressed in terms of the Carathéodory metric and the Möbius distance. This in turn answers a question by Paulsen for tuples of 2×2 matrices. We also establish von Neumann’s inequality for an n-tuple of upper triangular Toeplitz matrices. We study the regularity of KΩ(T) and MΩ(T) and obtain various comparisons of these two quantities when T is an n-tuple of Jordan blocks.

Original languageEnglish (US)
Pages (from-to)1095-1116
Number of pages22
JournalRocky Mountain Journal of Mathematics
Issue number4
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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