Tilbake til søkeresultatene

# Geometry of some non-classical Banach spaces.

#### Tildelt: kr 60 000

Prosjektnummer:

309597

Prosjektperiode:

2020 - 2021

Organisasjon:

Geografi:

Fagområder:

Samarbeidsland:

The project focuses on open research questions connected to the geometry of non-classial Banach spaces of type Müntz and Schreier. Some of the questions are intimately linked to a modern and active research direction in Banach space theory where different geometric properties of Banach spaces called diameter 2 properties, are considered. The reason for this is that diameter 2 properties and octahedrality properties are often dual properties in the sense that a Banach space has a diameter 2 property if and only the dual has an octahedrality property. Other questions are connected to extreme points in the unit ball of non-classical Müntz spaces, and one question is does in the direction of non-linear embeddings of Schreier spaces into Banach spaces. Together with the French partner team we want to explore the following questions: 1. Characterize the extreme points of the unit ball of the dual of a Müntz space. 2. Characterize the extreme points of the unit ball of a Müntz space. 3. Investigate when the dual of a Müntz space is L-embedded. 4. Investigate when Müntz spaces X as subspaces of the space of integrable functons on the unit interval are octahedral. 5. Characterize the extreme points of the unit ball of the Müntz spaces X in Question 4. 6. Does Lipschitz embedding with distortion < 2 of Schreier spaces X_(S_? ) into a Banach space X provide a corresponding lower bound in the Szlenk index of X?
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8199055790901184, "perplexity": 626.8648282520489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710155.67/warc/CC-MAIN-20221127005113-20221127035113-00265.warc.gz"}