On a Question of Arveson about Ranks of Hilbert modules

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dc.creatorFang, Xiang
dc.date2001-04-25
dc.date.accessioned2026-07-07T04:41:27Z
dc.date.available2026-07-07T04:41:27Z
dc.descriptionIt's well known that the functional Hilbert space over the unit ball in $B_{d} \in C^d$, with kernel function $K(z,w)=\frac{1}{1-z_{1}w_{1}-... -z_{d}w_{d}}$, admits a natural $A(B_{d})$-module structure. We show the rank of a nonzero submodule is infinity if and only if the submodule is of infinite codimension. Together with Arveson's dilation theory, our result shows that Hilbert modules stand in stark contrast with Hilbert basis theorem for algebraic modules. This result answers a question of Arveson.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0104246
dc.identifierhttp://arxiv.org/abs/math/0104246
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61366
dc.subjectOperator Algebras
dc.subject47A13
dc.titleOn a Question of Arveson about Ranks of Hilbert modules
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