Functionals on Banach Algebras with Scattered Spectra

H. S. Mustafayev. "Functionals on Banach Algebras with Scattered Spectra." Bulletin of the Polish Academy of Sciences. Mathematics 52.4 (2004): 395-403. <http://eudml.org/doc/280795>.

@article{H2004,
abstract = {Let A be a complex, commutative Banach algebra and let $M_A$ be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space $M_A$ is scattered (i.e., $M_A$ has no nonempty perfect subset). (b) Weakly almost periodic functionals on A with compact scattered spectra are almost periodic. (c) If $M_A$ is scattered, then the algebra A is Arens regular if and only if $A* = \overline\{span\} M_A$.},
author = {H. S. Mustafayev},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Banach algebra; group algebra; (weakly) almost periodic functional; scattered set},
language = {eng},
number = {4},
pages = {395-403},
title = {Functionals on Banach Algebras with Scattered Spectra},
url = {http://eudml.org/doc/280795},
volume = {52},
year = {2004},
}

TY - JOUR
AU - H. S. Mustafayev
TI - Functionals on Banach Algebras with Scattered Spectra
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 4
SP - 395
EP - 403
AB - Let A be a complex, commutative Banach algebra and let $M_A$ be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space $M_A$ is scattered (i.e., $M_A$ has no nonempty perfect subset). (b) Weakly almost periodic functionals on A with compact scattered spectra are almost periodic. (c) If $M_A$ is scattered, then the algebra A is Arens regular if and only if $A* = \overline{span} M_A$.
LA - eng
KW - Banach algebra; group algebra; (weakly) almost periodic functional; scattered set
UR - http://eudml.org/doc/280795
ER -