Maximal Contractive Tuples |
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Authors: | B Krishna Das Jaydeb Sarkar Santanu Sarkar |
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Institution: | 1. Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India 2. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India
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Abstract: | Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained. |
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