Weakly \mathcal U(d)-homogeneous commuting tuple of bounded operators

2025/12/09 by Ghara, Soumitra, Kumar, Surjit, Trivedi, Shailesh
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Operator Algebra Research

paper · doi:10.48550/arxiv.2512.08649

Abstract

We introduce and study the weakly \mathcal U(d)-homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly \mathcal U(d)-homogeneous tuple is similar to a \mathcal U(d)-homogeneous tuple. Further, we focus our attention to multishifts and completely characterize weakly \mathcal U(d)-homogeneous multishifts. In particular, we show that a multishift is weakly \mathcal U(d)-homogeneous if and only if it similar to a \mathcal U(d)-homogeneous multishift. The results for multishifts are further refined for the class of spherically balanced multishifts.

Citations

• A short note on similarity of operator-valued multishifts
• Commuting Tuple of Multiplication Operators Homogeneous under the Unitary Group
• Unitary equivalence of operator-valued multishifts
• The orbit of a bounded operator under the Möbius group modulo similarity equivalence
• Von Neumann's inequality for commuting operator-valued multishifts
• Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains
• Homogeneous Vector Bundles and intertwining Operators for Symmetric\n Domains
• A classification of homogeneous operators in the Cowen-Douglas class

Related

• Commuting Tuple of Multiplication Operators Homogeneous under the Unitary Group
• On the irreducibility and weakly homogeneity of a class of operators
• On extensions of commuting tuples of symmetric and isometric operators
• Homogeneous 2-shifts
• The orbit of a bounded operator under the Möbius group modulo similarity equivalence