Print Email Facebook Twitter The Grothendieck property of Weak Lp spaces and Marcinkiewicz spaces Title The Grothendieck property of Weak Lp spaces and Marcinkiewicz spaces Author van den Bosch, Pascal (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor de Pagter, B. (mentor) Veraar, M.C. (graduation committee) Kraaij, R.C. (graduation committee) de Jeu, M (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2019-03-01 Abstract In this master thesis the proof of Lotz that Weak Lp spaces have the Grothendieck property is studied. The proof is slightly modified to be more explicit and easier to comprehend by introducing lemma’s to better separate different parts of the proof that more clearly reveal its structure. Furthermore, the more general Marcinkiewicz spaces are shown to sometimes have the Grothendieck property, using the sufficient conditions for a Banach lattice to have the Grothendieck property that Lotz derived to prove the Grothendieck property of Weak Lp spaces. For most of these conditions that together are sufficient, proving that Marcinkiewicz spaces satisfy them is done in a way very similar to the case of Weak Lp spaces. However, the proof of the (necessary) condition that the dual sometimes has order continuous norm does not allow for such a simple generalization and requires more work. Finally, by using some more recent results about the existence of symmetric functionals in the dual, the conditions that are given for the Grothendieck property of Marcinkiewicz spaces are shown to be necessary, and we thereby obtain a characterization of the Marcinkiewicz spaces that have the Grothendieck property Subject grothendieck propertymarcinkiewicz spaceweak lp space To reference this document use: http://resolver.tudelft.nl/uuid:fbb37593-56dd-46ce-af07-92689af74d77 Part of collection Student theses Document type master thesis Rights © 2019 Pascal van den Bosch Files PDF verslag.pdf 536.46 KB Close viewer /islandora/object/uuid:fbb37593-56dd-46ce-af07-92689af74d77/datastream/OBJ/view