On the algebra of smooth operators
Volume 218 / 2013
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 $s$.
