TY - JOUR
AU - Popescu, Gelu
AB - Abstract We characterize the minimal isometric dilation of a non-commutative contractive sequence of operators as a universal object for certain diagrams of completely positive maps. A non-spatial construction of the minimal isometric dilation is also given, using Hilbert modules over C*-algebras. It is shown that the non-commutative disc algebras An (n≥2) are the universal algebras generated by contractive sequences of operators and the identity, and C*(S1, …, Sn) (n≥2), the extension through compact operators of the Cuntz algebra On, is the universal C*-algebra generated by a contractive sequence of isometries. It is also shown that the algebras An and C*(S1, …, Sn) are completely isometrically isomorphic to some free operator algebras considered by D. Blecher. In particular, the universal operator algebra of a row (respectively column) contraction is identified with a subalgebra of C*(S1, …, Sn). The internal characterization of the matrix norm on a universal algebra leads to some factorization theorems. © The London Mathematical Society
TI - Universal Operator Algebras Associated to Contractive Sequences of Non-Commuting Operators
JO - Journal of the London Mathematical Society
DO - 10.1112/S0024610798006656
DA - 1998-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/universal-operator-algebras-associated-to-contractive-sequences-of-non-t52EMe0br1
SP - 467
EP - 479
VL - 58
IS - 2
DP - DeepDyve
ER -