Abstract
Unbounded Linear Operators on Interpolation Spaces Kerstin Gunther, TU Berlin, Germany The operators S0, S1, S∆ and SΣ appearing in the classical interpolation theory are bounded and it holds SΣ = S. Similar to the classical interpolation theory, we introduce in general unbounded operators S0, S1, S∆ and SΣ. In this case, SΣ and S are not necessarily equal. If the operators S0, S1, S∆ and SΣ are bounded, then they coincide with the operators usually considered in the classical interpolation theory. We investigate the operators S0, S1, S∆, SΣ, S and induced operators on interpolation spaces. Of particular interest are spectral properties, Fredholm properties and the generalization of the local uniqueness-of-resolvent condition of T.J. Ransford.
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