On the algebra of smooth operators
Functional Analysis
2013-04-29 v1
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.
Cite
@article{arxiv.1304.7189,
title = {On the algebra of smooth operators},
author = {Tomasz Ciaś},
journal= {arXiv preprint arXiv:1304.7189},
year = {2013}
}