Old and new results on Allan's GB*-algebras

Maria Fragoulopoulou, Atsushi Inoue, and Klaus-Detlef Kürsten. "Old and new results on Allan's GB*-algebras." Banach Center Publications 91.1 (2010): 169-178. <http://eudml.org/doc/282372>.

@article{MariaFragoulopoulou2010,
abstract = {This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication of 𝓐₀ jointly continuous. We conclude that such a completion is a GB*-algebra over the τ-closure of the unit ball of 𝓐₀[||·||₀]. Further, we discuss some consequences of this result; we briefly comment the case when τ makes the multiplication of 𝓐₀ separately continuous and illustrate the results by examples.},
author = {Maria Fragoulopoulou, Atsushi Inoue, Klaus-Detlef Kürsten},
journal = {Banach Center Publications},
keywords = {unbounded operators; -algebras; locally convex -algebra},
language = {eng},
number = {1},
pages = {169-178},
title = {Old and new results on Allan's GB*-algebras},
url = {http://eudml.org/doc/282372},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Maria Fragoulopoulou
AU - Atsushi Inoue
AU - Klaus-Detlef Kürsten
TI - Old and new results on Allan's GB*-algebras
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 169
EP - 178
AB - This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication of 𝓐₀ jointly continuous. We conclude that such a completion is a GB*-algebra over the τ-closure of the unit ball of 𝓐₀[||·||₀]. Further, we discuss some consequences of this result; we briefly comment the case when τ makes the multiplication of 𝓐₀ separately continuous and illustrate the results by examples.
LA - eng
KW - unbounded operators; -algebras; locally convex -algebra
UR - http://eudml.org/doc/282372
ER -