English

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.

Keywords

Cite

@article{arxiv.1304.7189,
  title  = {On the algebra of smooth operators},
  author = {Tomasz Ciaś},
  journal= {arXiv preprint arXiv:1304.7189},
  year   = {2013}
}
R2 v1 2026-06-22T00:06:59.690Z