Abstract/Details

SUBALGEBRAS OF H('INFINITY) AND THE CORONA PROPERTY

RILEY, JOHN HENRY, JR. 
 University of Connecticut ProQuest Dissertations Publishing,  1980. 8103230.

Abstract (summary)

This dissertation is an investigation of subalgebras of H('(INFIN)), the Banach algebra of bounded analytic functions on the open unit disk, with respect to the corona property. That is, if B is a closed subalgebra of H('(INFIN)), is the open unit disk w*-dense in the maximal ideal space of B? Recent research has shown that for some subalgebras this is true while for others it is not. A major achievement of the dissertation is a theorem which relates the corona property to the polynomial convexity of cluster sets of functions of the subalgebra in question. The proof of this theorem depends upon certain facts concerning the fibers and fiber algebras of a subalgebra of H('(INFIN)). These are established and independently are of some interest.

Finally some examples of subalgebras with and without the corona property are produced. Previously known examples are investigated in light of the characterization mentioned above. New examples are exhibited which show that the corona property is not related to familiar concepts used in dealing with subalgebras of H('(INFIN)).

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
SUBALGEBRAS OF H('INFINITY) AND THE CORONA PROPERTY
Author
RILEY, JOHN HENRY, JR.
Number of pages
91
Degree date
1980
School code
0056
Source
DAI-B 41/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-204-69996-0
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8103230
ProQuest document ID
302970188
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/302970188/abstract