Unital strongly harmonic commutative Banach algebras

Janko Bračič. "Unital strongly harmonic commutative Banach algebras." Studia Mathematica 149.3 (2002): 253-266. <http://eudml.org/doc/285271>.

@article{JankoBračič2002,
abstract = {A unital commutative Banach algebra is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra is spectrally separable if there are enough elements in such that the corresponding multiplication operators on have the decomposition property (δ). On the other hand, if is spectrally separable, then for each a ∈ and each Banach left -module the corresponding multiplication operator $L_\{a\}$ on is super-decomposable. These two statements improve an earlier result of Baskakov.},
author = {Janko Bračič},
journal = {Studia Mathematica},
keywords = {Banach module; commutative Banach algebra; decomposition property ; multiplication operator; spectrally separable algebra; strongly harmonic algebra; super-decomposable operator},
language = {eng},
number = {3},
pages = {253-266},
title = {Unital strongly harmonic commutative Banach algebras},
url = {http://eudml.org/doc/285271},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Janko Bračič
TI - Unital strongly harmonic commutative Banach algebras
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 3
SP - 253
EP - 266
AB - A unital commutative Banach algebra is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra is spectrally separable if there are enough elements in such that the corresponding multiplication operators on have the decomposition property (δ). On the other hand, if is spectrally separable, then for each a ∈ and each Banach left -module the corresponding multiplication operator $L_{a}$ on is super-decomposable. These two statements improve an earlier result of Baskakov.
LA - eng
KW - Banach module; commutative Banach algebra; decomposition property ; multiplication operator; spectrally separable algebra; strongly harmonic algebra; super-decomposable operator
UR - http://eudml.org/doc/285271
ER -