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

Maria Fragoulopoulou; Atsushi Inoue; Klaus-Detlef Kürsten

Banach Center Publications (2010)

- Volume: 91, Issue: 1, page 169-178
- ISSN: 0137-6934

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topMaria 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 -

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