Hilbert modules over semicrossed products of the disk algebra

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dc.contributor.advisor Justin R. Peters
dc.contributor.author Buske, Dale
dc.contributor.department Mathematics
dc.date 2018-08-23T06:31:13.000
dc.date.accessioned 2020-06-30T07:15:40Z
dc.date.available 2020-06-30T07:15:40Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 1997
dc.date.issued 1997
dc.description.abstract <p>Given the disk algebra A( I !D) and an automorphism [alpha], there is associated a non-self-adjoint norm closed subalgebra doubz+x[alpha]A( I !D) of the crossed product doubzx[alpha]C( T) called the semicrossed product of A( I !D) with [alpha]. It is well known that the automorphisms of A( I !D) arise via composition with conformal bijections [phi] of I !D. These automorphisms are labeled according to the corresponding conformal maps as parabolic, hyperbolic, or elliptic and each case is studied. The contractive and completely contractive representations of doubz+x[alpha]A( I !D) on a Hilbert space H (i.e. contractive Hilbert modules) are found to be in a one-to-one correspondence with pairs of contractions S and T on H satisfying TS=S[phi](T). To this end, a noncommutative dilation result is obtained. It states that given a pair of contractions S and T on H satisfying TS=S[phi](T) there exist a pair of unitaries U and V on K supseteqH satisfying VU=U[phi](V) and dilating S and T respectively. Some concrete representations of doubz+x[alpha]A( I !D) are then found in order to compute the characters, the maximal ideal space, and the strong radical. The Shilov and orthoprojective Hilbert modules over doubz+x[alpha]A( I !D) are shown to correspond to pairs of isometries S and T satisfying TS=S[phi](T).</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/11778/
dc.identifier.articleid 12777
dc.identifier.contextkey 6510252
dc.identifier.doi https://doi.org/10.31274/rtd-180813-10706
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/11778
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/65072
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/11778/r_9737692.pdf|||Fri Jan 14 18:57:55 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics
dc.title Hilbert modules over semicrossed products of the disk algebra
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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