111 research outputs found
Characteristic functions and joint invariant subspaces
Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that
T is a completely non-coisometric row contraction. We establish the existence
of a "one-to-one" correspondence between the joint invariant subspaces under
T_1,..., T_n, and the regular factorizations of the characteristic function
associated with T. In particular, we prove that there is a non-trivial joint
invariant subspace under the operators T_1,..., T_n, if and only if there is a
non-trivial regular factorization of the characteristic function. We also
provide a functional model for the joint invariant subspaces in terms of the
regular factorizations of the characteristic function, and prove the existence
of joint invariant subspaces for certain classes of n-tuples of operators.
We obtain criterions for joint similarity of n-tuples of operators to Cuntz
row isometries. In particular, we prove that a completely non-coisometric row
contraction T is jointly similar to a Cuntz row isometry if and only if the
characteristic function of T is an invertible multi-analytic operator.Comment: 35 page
Free pluriharmonic majorants and noncommutative interpolation
In this paper, we initiate the study of sub-pluriharmonic curves in
Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative
balls. We are lead to a characterization of the noncommutative Hardy space
in terms of free pluriharmonic majorants, and to a Schur type
description of the unit ball of . These results are used to
solve a multivariable commutant lifting problem and provide a description of
all solutions.Comment: 35 page
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