Title: The Ces`aro operator: shift semigroups and invariant subspaces
Abstract: Despite the fact that one of the most classical transformations of sequences is the Ces`aro operator C, there are still many questions about it unsettled. In the seventies, Kriete and Trutt proved the striking result that the Ces`aro 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 J. R. Partington and W. T. Ross.
Zoom link to live sessions: https://uiowa.zoom.us/j/95316149275
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