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arXiv · 2103.05352

The multiplier algebra of the noncommutative Schwartz space

Tomasz Ciaś·Krzysztof Piszczek
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Abstract

We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest ${}^*$-algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly decreasing functions as the domain. We show in particular that it is neither a $\mathcal{Q}$-algebra nor $m$-convex. On the other hand, we prove that classical tools of functional analysis, for example, the closed graph theorem, the open mapping theorem or the uniform boundedness principle, are still available.

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Tomasz Ciaś, Krzysztof Piszczek. 2021-03-09. The multiplier algebra of the noncommutative Schwartz space. https://doi.org/10.1215/17358787-2017-0007

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