
Methods of function theory and Banach algebras in operator theory V. (GA1407880S)
from 01/01/2014
to 31/12/2016 investigator

Objectives:
The objectives of the present research project are investigations concerning:
1. orbits of operators, linear dynamics, invariant subspaces;
2. operator theory in function spaces;
3. operator positivity in matrix theory.



Holomorphic function spaces and their operators (MEB021108)
from 01/01/2011
to 31/12/2012 main investigator

Programme type: MOBILITY  France
Objectives:
Study of holomorphic functions spaces and related operators (Toeplitz, Hankel, Bergman projection, etc.) and their interplay with the Berezin transform. Where appropriate, extensions to spaces of harmonic functions may also be investigated.



Methods of function theory and Banach algebras in operator theory IV (201/09/0473)
from 01/01/2009
to 31/12/2014 investigator

Objectives:
The objectives of the present research project are investigations concerning: 1. existence of invariant subspaces and subsets with given properties; 2. operator theory in spaces of holomorphic functions; 3. orbits of operators, hypercyclic and supercyclic vectors, semigroups of operators; 4. interpolation problems, operator models and commutant lifting theorem.



Function theory and operator theory in Bergman spaces (IAA100190802)
from 01/01/2008
to 31/12/2011 main investigator

Operator theory and function theory in Bergman spaces is a relatively new and very active area of functional analysis which has close ties with other branches of mathematics (complex analysis, partial differential equations, group representations). The proposed project would concentrate on three topics in this area: Berezin transforms associated to spaces of holomorphic and nonholomorphic functions; function spaces and operators on bounded symmetric domains; and boundary singularities of weighted Bergman kernels. All these problems have applications in mathematical physics (quantization on Kähler manifolds), operator theory, complex geometry, and other fields.



Methods of function theory and Banach algebras in operator theory III. (201/06/0128)
from 01/01/2006
to 31/12/2008 investigator

The objectives of the present research project are investigations concerning: 1. existence of invariant subspaces and subsets with given properties; 2. operator theory in spaces of holomorphic functions; 3. orbits of operators, hypercyclic and supercyclic vectors, semigroups of operators; 4. interpolation problems, operator models and commutant lifting theorem.
