On the algebra of smooth operators

Volume 218 / 2013

Tomasz Ciaś Studia Mathematica 218 (2013), 145-166 MSC: Primary 46H35, 46J25, 46H30; Secondary 46H15, 46K10, 46A11, 46L05. DOI: 10.4064/sm218-2-3

Abstract

Let $s$ be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra $L(s',s)$ of so-called smooth operators. We also characterize closed commutative ${}^*$-subalgebras of $L(s',s)$ and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of $s$.

Authors

  • Tomasz CiaśFaculty of Mathematics and Computer Science
    A. Mickiewicz University in Poznań
    Umultowska 87
    61-614 Poznań, Poland
    e-mail

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