Hilbert modules over semicrossed products of the disk algebra
Hilbert modules over semicrossed products of the disk algebra
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 |
File
Original bundle
1 - 1 of 1