Maximal subalgebra of Douglas algebra
When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of H∞[q¯] to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)⋂Z(q) is not open in Z(q), we also find a cond...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000894 |
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| author | Carroll J. Gullory |
| author_facet | Carroll J. Gullory |
| author_sort | Carroll J. Gullory |
| collection | DOAJ |
| description | When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of H∞[q¯] to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)⋂Z(q) is not open in Z(q), we also find a condition that guarantees the existence of a factor q0 of q in H∞ such that B is maximal in H∞[q¯]. We also give conditions that show when two arbitrary Douglas algebras A and B, with A⫅B have property that A is maximal in B. |
| format | Article |
| id | doaj-art-61ec6336ce9b4fc38ea8f55c94677a82 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-61ec6336ce9b4fc38ea8f55c94677a822025-02-03T01:02:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111473574110.1155/S0161171288000894Maximal subalgebra of Douglas algebraCarroll J. Gullory0Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USAWhen q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of H∞[q¯] to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)⋂Z(q) is not open in Z(q), we also find a condition that guarantees the existence of a factor q0 of q in H∞ such that B is maximal in H∞[q¯]. We also give conditions that show when two arbitrary Douglas algebras A and B, with A⫅B have property that A is maximal in B.http://dx.doi.org/10.1155/S0161171288000894maximal subalgebraDouglas algebrainterpolating sequencesparse sequenceBlaschke productinner functionsopen and closed subsetnonanalytic pointssupport setQ−C level sets. |
| spellingShingle | Carroll J. Gullory Maximal subalgebra of Douglas algebra International Journal of Mathematics and Mathematical Sciences maximal subalgebra Douglas algebra interpolating sequence sparse sequence Blaschke product inner functions open and closed subset nonanalytic points support set Q−C level sets. |
| title | Maximal subalgebra of Douglas algebra |
| title_full | Maximal subalgebra of Douglas algebra |
| title_fullStr | Maximal subalgebra of Douglas algebra |
| title_full_unstemmed | Maximal subalgebra of Douglas algebra |
| title_short | Maximal subalgebra of Douglas algebra |
| title_sort | maximal subalgebra of douglas algebra |
| topic | maximal subalgebra Douglas algebra interpolating sequence sparse sequence Blaschke product inner functions open and closed subset nonanalytic points support set Q−C level sets. |
| url | http://dx.doi.org/10.1155/S0161171288000894 |
| work_keys_str_mv | AT carrolljgullory maximalsubalgebraofdouglasalgebra |