Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review
The notion of (unbounded) C*-seminorms plays a relevant role in the representation theory of *-algebras and partial *-algebras. A rather complete analysis of the case of *-algebras has given rise to a series of interesting concepts like that of semifinite C*-seminorm and spectral C*-seminorm that gi...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/79268 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850172751277457408 |
|---|---|
| author | Camillo Trapani |
| author_facet | Camillo Trapani |
| author_sort | Camillo Trapani |
| collection | DOAJ |
| description | The notion of (unbounded) C*-seminorms plays a relevant role in the representation theory of *-algebras and partial *-algebras. A rather complete analysis of the case of *-algebras has given rise to a series of interesting concepts like that of semifinite
C*-seminorm and spectral C*-seminorm that give information on the properties of
*-representations of the given *-algebra A and also on the structure of the *-algebra itself, in particular when
A is endowed with a locally convex topology. Some of these results extend to partial *-algebras too. The state of the art on this topic is reviewed in this paper, where the possibility of constructing unbounded C*-seminorms from certain families of positive sesquilinear forms, called biweights, on a (partial)
*-algebra A is also discussed. |
| format | Article |
| id | doaj-art-d4a82db6dcb042f5a13d8e39f4a3798b |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d4a82db6dcb042f5a13d8e39f4a3798b2025-08-20T02:20:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/7926879268Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A reviewCamillo Trapani0Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo 90123, ItalyThe notion of (unbounded) C*-seminorms plays a relevant role in the representation theory of *-algebras and partial *-algebras. A rather complete analysis of the case of *-algebras has given rise to a series of interesting concepts like that of semifinite C*-seminorm and spectral C*-seminorm that give information on the properties of *-representations of the given *-algebra A and also on the structure of the *-algebra itself, in particular when A is endowed with a locally convex topology. Some of these results extend to partial *-algebras too. The state of the art on this topic is reviewed in this paper, where the possibility of constructing unbounded C*-seminorms from certain families of positive sesquilinear forms, called biweights, on a (partial) *-algebra A is also discussed.http://dx.doi.org/10.1155/IJMMS/2006/79268 |
| spellingShingle | Camillo Trapani Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review International Journal of Mathematics and Mathematical Sciences |
| title | Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review |
| title_full | Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review |
| title_fullStr | Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review |
| title_full_unstemmed | Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review |
| title_short | Unbounded C*-seminorms, biweights, and *-representations of partial *-algebras: A review |
| title_sort | unbounded c seminorms biweights and representations of partial algebras a review |
| url | http://dx.doi.org/10.1155/IJMMS/2006/79268 |
| work_keys_str_mv | AT camillotrapani unboundedcseminormsbiweightsandrepresentationsofpartialalgebrasareview |