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Hannes Thiel: The zero-product structure of C*-algebras

GOAT (Grupp och operator algebror träff)

Time: Mon 2022-09-12 15.15 - 16.15

Location: Albano, Carmérrumet

Participating: Hannes Thiel (CAU Kiel)

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It is well-known that every C*-algebra is determined by its linear and multiplicative structure: Two C*-algebras are *-isomorphic if and only if they admit a multiplicative, linear bijection.
We study if instead of the whole multiplicative structure it suffices to record when two elements have zero product. While it is not clear if every C*-algebra is determined this way, we obtain many positive results. In particular, two unital, simple C*-algebras are *-isomorphic if and only if they admit a linear bijection that preserves zero products.

This is joint work with Eusebio Gardella.