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A Constructive Approach to the Universality Criterion for Semigroups

Walmsley, David
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490028671735536

Abstract Details

2017, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics.
We prove a generalization of the well-known Universality Criterion in the setting of continuous homomorphisms acting on a separable, complete, metrizable topological semigroup by constructing a particular universal element. Consequently, we simplify the proof of a 1955 classical result of Heins on the existence of universal Blaschke products on the unit ball of bounded analytic functions on the open unit disk, and the proofs of a number of other related results, by unifying them in the semigroup setting. Motivated by our generalization, we provide new applications such as the homomorphisms of conjugation on the unit ball of the operator algebra of c0 and ℓp, where 1≤ p<∞, and also the homomorphisms of composition on the closed unit ball of L∞[0,1] with the weak-star topology, as well as on the semigroup of all measurable integrable functions bounded in sup-norm by 1.
Kit Chan (Advisor)
John Laird (Other)
Juan Bes (Committee Member)
Alex Izzo (Committee Member)
62 p.
Mathematics
Universality Criterion; Topological Semigroup; Blaschke Product; Composition Operator

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Citations

  • Walmsley, D. (2017). A Constructive Approach to the Universality Criterion for Semigroups [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490028671735536

    APA Style (7th edition)

  • Walmsley, David. A Constructive Approach to the Universality Criterion for Semigroups. 2017. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490028671735536.

    MLA Style (8th edition)

  • Walmsley, David. "A Constructive Approach to the Universality Criterion for Semigroups." Doctoral dissertation, Bowling Green State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1490028671735536

    Chicago Manual of Style (17th edition)

bgsu1490028671735536
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This open access ETD is published by Bowling Green State University and OhioLINK.