Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
NONCOMMUTATIVE INTERPOLATION AND POISSON TRANSFORMS
 

Summary: NONCOMMUTATIVE INTERPOLATION
AND POISSON TRANSFORMS
Alvaro Arias and Gelu Popescu
Abstract. Generalresultsof interpolation(eg. Nevanlinna-Pick)by elementsin the
noncommutative analytic Toeplitz algebra F1 (resp. noncommutative disc algebra
An) with consequences to the interpolation by bounded operator-valued analytic
functions in the unit ball of Cn are obtained.
Non-commutativePoisson transformsare used to provide new von Neumann type
inequalities. Completely isometric representations of the quotient algebra F1=J on
Hilbert spaces, where J is any w -closed, 2-sided ideal of F1, are obtained and used
to construct a w -continuous, F1=J{functional calculus associated to row contrac-
tions T = T1 : :: Tn] when f(T1 : :: Tn) = 0 for any f 2 J. Other properties of
the dual algebra F1=J are considered.
In Po5], the second author proved the following version of von Neumann's in-
equality for row contractions: if T1 ::: Tn 2 B(H) (the algebra of all bounded
linear operators on the Hilbert space H) and T = T1 ::: Tn] is a contraction, i.e.,
Pn
i=1 TiTi IH, then for every polynomial p(X1 ::: Xn) on n noncommuting
indeterminates,
(1) p(T1 ::: Tn) B(H) p(S1 ::: Sn) B(F2)

  

Source: Arias, Alvaro - Department of Mathematics, University of Denver

 

Collections: Mathematics