1997/09/11 by Arias, Alvaro, Popescu, Gelu
#47D25 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.math/9709213
General results of interpolation (eg. Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebra F^∞ (resp. noncommutative disc algebra An) with consequences to the interpolation by bounded operator-valued analytic functions in the unit ball of \bf Cn are obtained. Non-commutative Poisson transforms are used to provide new von Neumann type inequalities. Completely isometric representations of the quotient algebra F^∞/J on Hilbert spaces, where J is any w^*-closed, 2-sided ideal of F^∞, are obtained and used to construct a w^*-continuous, F^∞/J--functional calculus associated to row contractions T=[T1,…, Tn] when f(T1,…,Tn)=0 for any f∈ J. Other properties of the dual algebra F^∞/J are considered.