Abstract
We calculate the measure of non-compactness of the multiplication operator \(M_u\) acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of \(M_u\) acting on Köthe spaces.
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Communicated by Mohammad Sal Moslehian.
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Castillo, R.E., Rafeiro, H., Ramos-Fernández, J.C. et al. Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range. Bull. Malays. Math. Sci. Soc. 42, 1523–1534 (2019). https://doi.org/10.1007/s40840-017-0562-0
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DOI: https://doi.org/10.1007/s40840-017-0562-0