Operator-valued inner functions analytic on the closed disc

Hardy space of operator-valued analytic functions

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...

Operator-valued Bergman Inner Functions as Transfer Functions

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

On Closed Ideals of Analytic Functions

1. The closed ideals in the algebra A of all continuous functions fieie) on the unit circle X = {eie: 0^.B<2ir] which have analytic extensions/(z), \z\ <1 have been determined by Beurling and independently by Rudin [5] as follows: Let Hx denote the weak* closure [A]* of A as a subset of Laidm), where m denotes the normalized Lebesgue measure dd/2ir on the circle. A function qEHTM is called inne...

Operator-valued tensors on manifolds

‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian...

On the differential structure of matrix–valued rational inner functions