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Θα\nεξετάσουμε ποιοι κλασικοί χώροι Banach είναι χώροι C(K) (ως προς ισομετρικό ισομορφισμό) και την ταξινόμησή τους ως προς γραμμικό ισομορφισμό. Θα μελετήσουμε επίσης την weak-συμπάγεια υποσυνόλων και τελεστών στους χώρους C(K) αλλά και στον L1(μ).\nΣτο δεύτερο μέρος θα μιλήσουμε για διανυσματικά μέτρα, δηλαδή μέτρα με πεδίο τιμών χώρους Banach και θα εξετάσουμε πότε μπορούμε να έχουμε ένα διανυσματικό θεώρημα Radon-Nikodym και ποιες είναι οι ιδιότητες των χώρων στους οποίους ισχύει ένα τέτοιο θεώρημα." }, { "@language" : "en", "@value" : "This dissertation consists of two parts:\nIn the first part we will focus on C(K) spaces, where K is a compact Hausdorff\ntopological space, and we will study their properties as Banach spaces. We will\nfocus on which common Banach spaces are C(K) spaces (in terms of isometric isomorphism) and their classification under linear isomorphism. 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