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The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized.
Camillo Trapani. "C*-seminorms on partial *-algebras: an overview." Banach Center Publications 67.1 (2005): 369-384. <http://eudml.org/doc/282492>.
@article{CamilloTrapani2005, abstract = {The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized.}, author = {Camillo Trapani}, journal = {Banach Center Publications}, keywords = {unbounded -seminorms; partial *-algebras; quasi *-algebras; biweights}, language = {eng}, number = {1}, pages = {369-384}, title = {C*-seminorms on partial *-algebras: an overview}, url = {http://eudml.org/doc/282492}, volume = {67}, year = {2005}, }
TY - JOUR AU - Camillo Trapani TI - C*-seminorms on partial *-algebras: an overview JO - Banach Center Publications PY - 2005 VL - 67 IS - 1 SP - 369 EP - 384 AB - The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized. LA - eng KW - unbounded -seminorms; partial *-algebras; quasi *-algebras; biweights UR - http://eudml.org/doc/282492 ER -