Abstract
The S-functional calculus can also be de_ned for unbounded operators T : D(T) _ X ! X, where X is a two-sided quaternionic Banach space X. In the papers [69,101] this calculus was de_ned using suitable transformations in order to reduce the problem to the case of bounded operators. The direct approach has been studied in the more recent paper [130] and it turned out that the two approaches, contrary to the complex setting, are not totally equivalent. In fact, in using the direct approach one can remove the assumption that the S-resolvent set contains a real point.
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Colombo, F., Gantner, J. (2019). The direct approach to the S-functional calculus. In: Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes. Operator Theory: Advances and Applications, vol 274. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-16409-6_3
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DOI: https://doi.org/10.1007/978-3-030-16409-6_3
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Publisher Name: Birkhäuser, Cham
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