The lattice of C*-covers of an operator algebra
Faculty Advisor
Date
2025
Keywords
C*-cover, operator algebra, non-selfadjoint, lattice equivalences
Abstract (summary)
In this article, it is shown that the lattice of C ∗ -covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the lattice of C ∗ -covers are developed and proven to be distinct. The lattice of C ∗ -covers of direct sums and tensor products are studied. Along the way key examples are found of operator algebras, each of which generates exactly n C ∗ -algebras up to ∗-isomorphism, and a simple operator algebra that is not similar to a C ∗ -algebra.
Publication Information
Humeniuk, A., & Ramsey, C. (2025). The lattice of C*-covers of an operator algebra. Canadian Journal of Mathematics, 1-29. https://doi.org/10.4153/S0008414X25000045
Notes
Item Type
Article
Language
Rights
Attribution-NonCommercial (CC BY-NC)
