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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-2-3,
author = {Tomasz Cia\'s},
title = {On the algebra of smooth operators},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {145-166},
zbl = {1298.46042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-2-3}
}
Tomasz Ciaś. On the algebra of smooth operators. Studia Mathematica, Tome 215 (2013) pp. 145-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-2-3/