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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 $$d$$ d -dimensional unit ball $${\mathbb {B}}_d$$ B d is defined. For $$d=1$$ d = 1 , it is shown that every submodule of the Hardy module over the unit disc is maximal...
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