Poisson Transforms on SomeC*-Algebras Generated by Isometries

✍ Scribed by Gelu Popescu

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 259 KB
• Volume: 161
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3346

✦ Synopsis

A noncommutative Poisson transform associated to a certain class of sequences of operators on Hilbert spaces, with property (P), is defined on some universal C*-algebras (resp. nonselfadjoint algebras) generated by isometries. Its properties are described and used to study these universal algebras and their representations. As consequences, we obtain a functional calculus, isometric (resp. unitary) dilations, and commutant lifting theorem for the class of sequences of operators with property (P). Our ``geometrical'' approach leads also to new and elementary proofs as well as extensions of some classical results.