DESCRIPTIVE COMPLEXITIES IN POLISH SPACES OF SEPARABLE BANACH SPACES

Date

2025-8-07

Author

Kaplan, Anıl

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In this thesis, we will analyze various classes of separable Banach spaces from a descriptive set-theoretic point of view. In order to be able to do that, we will need to code separable Banach spaces as elements of a Polish space. There are various ways to do such a coding. In this thesis, we will overview the construction of two such Polish spaces, analyze their basic properties and investigate the relationship between them. Afterwards, we will compute the descriptive complexity of the isomorphism and the isometry classes of the separable Banach space 𝑙_2 in these spaces. Moreover, we shall give a characterization of the space 𝑙_2 up to isometry in one of these spaces. For these results, we shall mostly be following Godefroy and Saint-Raymond, and, Cúth et. al. Finally, we will overview some descriptive set theoretical results regarding other classical Banach spaces.

Subject Keywords

Separable Banach space, Polish space, Borel hierarchy, descriptive com plexity

URI

https://hdl.handle.net/11511/115531

Collections

Graduate School of Natural and Applied Sciences, Thesis