Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

E. Kaniuth, A. T. Lau, and A. Ülger. "Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras." Studia Mathematica 183.1 (2007): 35-62. <http://eudml.org/doc/285186>.

@article{E2007,
abstract = {Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.},
author = {E. Kaniuth, A. T. Lau, A. Ülger},
journal = {Studia Mathematica},
keywords = {Banach algebra; structure space; homomorphism; multiplier algebra; bounded approximate identity; second dual; Bochner-Schoenberg-Eberlein property; polar decomposition; locally compact groups; Fourier algebra},
language = {eng},
number = {1},
pages = {35-62},
title = {Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras},
url = {http://eudml.org/doc/285186},
volume = {183},
year = {2007},
}

TY - JOUR
AU - E. Kaniuth
AU - A. T. Lau
AU - A. Ülger
TI - Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras
JO - Studia Mathematica
PY - 2007
VL - 183
IS - 1
SP - 35
EP - 62
AB - Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.
LA - eng
KW - Banach algebra; structure space; homomorphism; multiplier algebra; bounded approximate identity; second dual; Bochner-Schoenberg-Eberlein property; polar decomposition; locally compact groups; Fourier algebra
UR - http://eudml.org/doc/285186
ER -