Geodesic
On the algebra of smooth operators
Tomasz Ciaś1
1Faculty of Mathematics and Computer Science A. Mickiewicz University in Poznań Umultowska 87 61-614 Poznań, Poland
Studia Mathematica, Tome 218 (2013) no. 2, pp. 145-166
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $s$.
DOI : 10.4064/sm218-2-3
Keywords: space rapidly decreasing sequences spectral representation normal elements chet algebra so called smooth operators characterize closed commutative * subalgebras establish nbsp lder continuous functional calculus algebra key tool property

Tomasz Ciaś  1

1 Faculty of Mathematics and Computer Science A. Mickiewicz University in Poznań Umultowska 87 61-614 Poznań, Poland 
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Tomasz Ciaś. On the algebra of smooth operators. Studia Mathematica, Tome 218 (2013) no. 2, pp. 145-166. doi: 10.4064/sm218-2-3

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