标题：Unbounded <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-seminorms, biweights, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-representations of partial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi></mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-algebras: A review
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/79268
出版社：Hindawi Publishing Corporation
摘要：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.
