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arXiv · 1304.7189

On the algebra of smooth operators

Tomasz Ciaś
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Abstract

Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fr\'echet algebra L(s',s) of the so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a H\"older continuous functional calculus in this algebra. The key tool is the property (DN) of s.

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Tomasz Ciaś. 2013-04-26. On the algebra of smooth operators. https://arxiv.org/abs/1304.7189

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