The Cesáro operator: shift semigroups and invariant subspaces

Eva A.Gallardo-Gutiérrez. Universidad Complutense de Madrid

Lunes 30/10, a las 16 hs. Sala de Conferencias DM-IMAS (2do piso Pab. I)


Abstract:  Despite the fact that one of the most classical transformations of sequences is the Cesàro operator C, there are still many questions about it unsettled.
In the seventies, Kriete and Trutt proved the striking result that the Cesàro operator is subnormal, namely, C has a normal extension. Nonetheless, it remains unknown the description of the closed invariant subspaces of C.
In this talk, we will discuss the invariant subspaces of C in the Hardy spaces. Moreover, in the Hilbert space setting, by linking the invariant sub-spaces of C to the lattice of the closed invariant subspaces of the standard right-shift semigroup acting on a particular weighted L2-space on the line, we will exhibit a large class of non-trivial closed invariant subspaces of C and provide a complete characterization of the finite codimensional ones. In particular, we will establish the limits of such approach in order to provide a complete description of the lattice of the invariant subspaces of C.

Based on joint works with Jonathan R. Partington and W. Ross.


Departamento de Matemática
Pabellón I - Ciudad Universitaria

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