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Elke Enning

Tomasz Kania (Warwick): When is multiplication in a Banach algebra open? Oberseminar C*-Algebren.

Veröffentlicht Thursday, 18.01.2018 08:52

Mathematik und Informatik

We contribute to the on-going project of determining for what functions spaces the operation of multiplication is an open map by putting our investigations on a more systematic footing of Banach-algebra theory. We demonstrate that should a Banach algebra have open multiplication, the group of invertible elements must be dense in it. As a result, we answer a question posed by Balcerzak, Behrends, and Strobin of whether the Cauchy product of absolutely convergent series (that is, convolution in the semigroup algebra of non-negative integers) is not open. By appealing to ultraproduct techniques and infinite abelian group theory, we demonstrate that neither in the group algebra of the integers nor in the group algebra of the rationals convolution is uniformly open. The problem of openness of multiplication in Banach algebras of bounded operators on Banach spaces and their Calkin algebras is also addressed. This is joint work with Szymon Draga (Diebold Nixdorf).



Angelegt am Thursday, 18.01.2018 08:52 von Elke Enning
Geändert am Thursday, 18.01.2018 08:52 von Elke Enning
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