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The lattice of C
$^*$-covers of an operator algebra
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 14 February 2025, pp. 1-29
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- Article
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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.
