Operators associated with a domain in \mathbb C⁴ and applications

2025/07/19 by Sourav Pal, Pal, Sourav, Nitin Tomar +1
Mathematics · #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2507.14589

openalex publication_date 2025/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The hexablock is a domain arising from a special case of the μ-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply \mathbb H-contraction. We characterize the unitaries and isometries associated with \mathbb H-contractions. Two different types of dilation results for \mathbb H-contractions are obtained. We find connection of this theory with the operators associated with the symmetrized bidisc and tetrablock, two other domains related to the μ-synthesis problem.

Citations

• A Schwarz lemma for the pentablock
• Common reducing subspaces and decompositions of contractions
• Rational tetra-inner functions and the special variety of the tetrablock
• Rational dilation of tetrablock contractions revisited
• Canonical decomposition of a tetrablock contraction and operator model
• The failure of rational dilation on the tetrablock
• Subvarieties of the tetrablock and von Neumann's inequality
• The group of automorphisms of the pentablock

Related

• The Hexablock: a domain associated with the μ-synthesis in M₂(\mathbb C)
• Common reducing subspaces and decompositions of contractions
• Triangular Tetrablock-contractions, factorization of contractions, dilation and subvarieties
• Rational dilation of tetrablock contractions revisited
• A note on the dilation of a certain family of tetrablock contractions