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Lifting Module Maps Between Different Noncommutative Domain Algebras

Summary: Lifting Module Maps Between Different
Noncommutative Domain Algebras
Alvaro Arias and Jonathan Von Stroh
University of Denver
December 6, 2010
In this paper we use a renorming technique to lift module maps be-
tween -invariant submodules of domain algebras. These algebras were
recently introduced by Popescu as non-selfadjoint operator algebras gen-
erated by some weighted shifts on the Full Fock space.
1 Introduction
In [12], Popescu studied noncommutative domains Df (H) B(H)n
by positive regular free holomorphic functions f. He proved that each such
domain has a universal model (W1, W2, . . . , Wn) of weighted orthogonal shifts
acting on the full Fock space with n generators 2(F+
n ). These algebras are nat-
ural generalizations of the algebras generated by the left creation operators on
the Full Fock space. Popescu proved that the domain algebras satisfy commu-
tant lifting theorems and have Poisson kernels, and as a result they satisfy the


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


Collections: Mathematics