Near invariance and kernels of Toeplitz operators |
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Authors: | M. Cristina Câmara Jonathan R. Partington |
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Affiliation: | 1. Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, 1049-001, Lisboa, Portugal 2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
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Abstract: | This paper makes a systematic study of kernels of Toeplitz operators on scalar and vector-valued H p spaces (for 1 < p < ∞). The property of near invariance of a kernel for the backward shift is analysed and shown to hold in increased generality. In the scalar case, and in some vectorial cases, the existence of a minimal kernel containing a given function is established, and a symbol for a corresponding Toeplitz operator is determined; thus, for rational symbols, its dimension can be easily calculated. It is shown that every Toeplitz kernel in H p is the minimal kernel for some function lying in it. |
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