Print Email Facebook Twitter Strongly continuous and locally equi-continuous semigroups on locally convex spaces Title Strongly continuous and locally equi-continuous semigroups on locally convex spaces Author Kraaij, R.C. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2015-02-07 Abstract We consider locally equi-continuous strongly continuous semigroups on locally convex spaces (X,?) that are also equipped with a ‘suitable’ auxiliary norm. We introduce the set N of ? -continuous semi-norms that are bounded by the norm. If (X,?) has the property that N is closed under countable convex combinations, then a number of Banach space results can be generalised in a straightforward way. Importantly, we extend the Hille–Yosida theorem. We relate our results to those on bi-continuous semigroups and show that they can be applied to semigroups on (Cb(E),?) and (B(H),?) for a Polish space E and a Hilbert space H and where ? is their respective strict topology. Subject algebra To reference this document use: http://resolver.tudelft.nl/uuid:b268d93c-baf3-4b9f-baa7-919efe03527d DOI https://doi.org/10.1007/s00233-015-9689-1 Publisher Springer ISSN 0037-1912 Source Semigroup Forum, 2015 Part of collection Institutional Repository Document type journal article Rights © 2015 The Author(s)This article is published with open access at Springerlink.com Files PDF Kraaij_2015.pdf 299.36 KB Close viewer /islandora/object/uuid:b268d93c-baf3-4b9f-baa7-919efe03527d/datastream/OBJ/view