On the algebra of smooth operators

Tomasz Ciaś. "On the algebra of smooth operators." Studia Mathematica 218.2 (2013): 145-166. <http://eudml.org/doc/286517>.

@article{TomaszCiaś2013,
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.},
author = {Tomasz Ciaś},
journal = {Studia Mathematica},
keywords = {topological algebra; involutive algebra; representations of algebras; functional calculus; nuclear Fréchet space; -algebra; smooth operator; space of rapidly decreasing sequences},
language = {eng},
number = {2},
pages = {145-166},
title = {On the algebra of smooth operators},
url = {http://eudml.org/doc/286517},
volume = {218},
year = {2013},
}

TY - JOUR
AU - Tomasz Ciaś
TI - On the algebra of smooth operators
JO - Studia Mathematica
PY - 2013
VL - 218
IS - 2
SP - 145
EP - 166
AB - 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.
LA - eng
KW - topological algebra; involutive algebra; representations of algebras; functional calculus; nuclear Fréchet space; -algebra; smooth operator; space of rapidly decreasing sequences
UR - http://eudml.org/doc/286517
ER -