2,702 research outputs found
Inner multipliers and Rudin type invariant subspaces
Let be a Hilbert space and be
the -valued Hardy space over the unit disc in
. The well known Beurling-Lax-Halmos theorem states that every
shift invariant subspace of other than
has the form , where is an
operator-valued inner multiplier in for some Hilbert space . In this
paper we identify with -valued Hardy
space and classify all such inner
multiplier for which is a Rudin type invariant subspace of
.Comment: 8 page
On certain Toeplitz operators and associated completely positive maps
We study Toeplitz operators with respect to a commuting -tuple of bounded
operators which satisfies some additional conditions coming from complex
geometry. Then we consider a particular such tuple on a function space. The
algebra of Toeplitz operators with respect to that particular tuple becomes
naturally homeomorphic to of a certain compact subset of . Dual Toeplitz operators are characterized. En route, we prove an
extension type theorem which is not only important for studying Toeplitz
operators, but also has an independent interest because dilation theorems do
not hold in general for .Comment: 25 pages. arXiv admin note: text overlap with arXiv:1706.0346
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