Abstract
A Toeplitz operator with symbol G such that det G = 1 is invertible if there is a non-trivial solution to a Riemann–Hilbert problem G ϕ + = ϕ − with ϕ + and ϕ − satisfying the corona conditions in C + and C − , respectively. However, determining such a solution and verifying that the corona conditions are satisfied are in general difficult problems. In this paper, on one hand, we establish conditions on ϕ ± which are equivalent to the corona conditions but easier to verify, if G ± 1 are analytic and bounded in a strip. This happens in particular with almost-periodic symbols. On the other hand, we identify new classes of symbols G for which a non-trivial solution to G ϕ + = ϕ − can be explicitly determined and the corona conditions can be verified by the above mentioned approach, thus obtaining invertibility criteria for the associated Toeplitz operators.
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