Fréchet algebras, formal power series, and automatic continuity

S. R. Patel. "Fréchet algebras, formal power series, and automatic continuity." Studia Mathematica 187.2 (2008): 125-136. <http://eudml.org/doc/284896>.

@article{S2008,
abstract = {We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra ℂ[[X]] in such a way that they contain the polynomials. It is shown that these algebras (except ℂ[[X]] itself) always satisfy a certain equicontinuity condition due to Loy. Using this result, some applications to the theory of automatic continuity are given; in particular, the uniqueness of the Fréchet algebra topology for such algebras is established.},
author = {S. R. Patel},
journal = {Studia Mathematica},
keywords = {Fréchet algebras of power series; automatic continuity},
language = {eng},
number = {2},
pages = {125-136},
title = {Fréchet algebras, formal power series, and automatic continuity},
url = {http://eudml.org/doc/284896},
volume = {187},
year = {2008},
}

TY - JOUR
AU - S. R. Patel
TI - Fréchet algebras, formal power series, and automatic continuity
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 2
SP - 125
EP - 136
AB - We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra ℂ[[X]] in such a way that they contain the polynomials. It is shown that these algebras (except ℂ[[X]] itself) always satisfy a certain equicontinuity condition due to Loy. Using this result, some applications to the theory of automatic continuity are given; in particular, the uniqueness of the Fréchet algebra topology for such algebras is established.
LA - eng
KW - Fréchet algebras of power series; automatic continuity
UR - http://eudml.org/doc/284896
ER -