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Virtual levels, also known as threshold resonances, admit several equivalentcharacterizations: (1) there are corresponding virtual states from a spaceslightly weaker than $L^2$; (2) there is no limiting absorption principle intheir vicinity (e.g. no weights such that the "sandwiched" resolvent isuniformly bounded); (3) an arbitrarily small perturbation can produce aneigenvalue. We develop a general approach to virtual levels in Banach spacesand provide applications to Schroedinger operators with nonselfadjointpotentials and in any dimension.

Virtual levels and virtual states of linear operators in Banach spaces. Applications to Schroedinger operators