{"id":{"repo_id":"tartu","oai_identifier":"oai:dspace.ut.ee:10062/115534"},"canonical_url":"https://search.dev.ndltd.org/etd/tartu/oai:dspace.ut.ee:10062/115534","repository":{"repo_id":"tartu","name":"University of Tartu","base_url":"http://dspace.ut.ee/oai/request"},"display":{"title":"Daugavet and Delta-points in Banach spaces: Lipschitz-free spaces, their duals, and renormings","abstract":"Daugaveti ja Delta-punktid on vastavalt Banachi ruumi Daugaveti omaduse ja diametraalse lokaalse diameeter-kahe omaduse punktilised versioonid. Mõlemad ruumide omadused kuuluvad diameeter-kaks omaduste klassi, mis tähendab, et iga ühikkera viilu diameeter on 2. Seevastu Daugaveti või Delta-punktide olemasolu ei nõua nii tugevaid globaalseid omadusi. Tõepoolest, leidub Banachi ruume, mis sisaldavad Daugaveti või Delta-punkte, kuid mille ühikkera viilud võivad olla kuitahes väikese diameetriga. Käesolevas väitekirjas uuritakse Daugaveti ja Delta-punkte erinevates Banachi ruumide klassides, sealhulgas Lipschitzi-vabades ruumides ja nende kaasruumides. Antakse iseloomustavad kriteeriumid nende ruumide teatud alamklassides, sealhulgas antakse Daugavet punktidele täielik kirjeldus kõigis Lipschitzi-vabades ruumides. Lisaks tuuakse näide meetrilisest ruumist, mille Lipschitzi-vaba ruum on Radon-Nikodými omadusega ning sisaldab ka Daugaveti punkti. Samuti näidatakse, et see Lipschitzi-vaba ruum on kaasruum, mis on isomorfne Banachi ruumiga ℓ1. Töös käsitletakse Banachi ruumide ümbernormeerimisi nii, et need sisaldavad Daugaveti või Delta-punkte. Selle tulemusena näidatakse, et klassikalised Banachi ruumid ℓp, kus pϵ[1,∞), on ümbernormeeritavad nii, et need sisaldavad Daugaveti punkte. See annab esimesed näited refleksiivsetest ruumidest, mis sisaldavad Daugaveti punkte. Lõpuks tuuakse välja mitmeid Banachi ruumide klasse, mis ei saa Daugaveti või Delta-punkte sisaldada.Daugavet and Delta-points were introduced as pointwise versions of the Daugavet property and the diametral local diameter-two property, respectively. Both of these properties belong to the class of diameter-two properties, meaning that every slice of the unit ball has diameter 2. In contrast, the mere existence of Daugavet or Delta-points does not imply such strong global properties. Indeed, there exist Banach spaces that contain Daugavet or Delta-points, but also admit slices of the unit ball with arbitrarily small diameter. In this thesis, we study Daugavet and Delta-points in various classes of Banach spaces, among these Lipschitz-free spaces and their duals. We provide characterizations for certain subclasses of these spaces, including a complete characterization of Daugavet points in Lipschitz-free spaces. Furthermore, we present an example of a metric space whose Lipschitz-free space has the Radon—Nikodým property and a Daugavet point. We also show that this Lipschitz-free space is a dual space, isomorphic to ℓ1. The thesis further investigates renormings of Banach spaces that admit Daugavet or Delta-points. As a result, we show that the classical spaces ℓp for pϵ[1,∞) can be renormed to contain a Daugavet point. This provides the first examples of reflexive spaces admitting Daugavet points. Finally, we introduce several classes of Banach spaces that cannot contain Daugavet or Delta-points.","abstract_html":"Daugaveti ja Delta-punktid on vastavalt Banachi ruumi Daugaveti omaduse ja diametraalse lokaalse diameeter-kahe omaduse punktilised versioonid. Mõlemad ruumide omadused kuuluvad diameeter-kaks omaduste klassi, mis tähendab, et iga ühikkera viilu diameeter on 2. Seevastu Daugaveti või Delta-punktide olemasolu ei nõua nii tugevaid globaalseid omadusi. Tõepoolest, leidub Banachi ruume, mis sisaldavad Daugaveti või Delta-punkte, kuid mille ühikkera viilud võivad olla kuitahes väikese diameetriga. Käesolevas väitekirjas uuritakse Daugaveti ja Delta-punkte erinevates Banachi ruumide klassides, sealhulgas Lipschitzi-vabades ruumides ja nende kaasruumides. Antakse iseloomustavad kriteeriumid nende ruumide teatud alamklassides, sealhulgas antakse Daugavet punktidele täielik kirjeldus kõigis Lipschitzi-vabades ruumides. Lisaks tuuakse näide meetrilisest ruumist, mille Lipschitzi-vaba ruum on Radon-Nikodými omadusega ning sisaldab ka Daugaveti punkti. Samuti näidatakse, et see Lipschitzi-vaba ruum on kaasruum, mis on isomorfne Banachi ruumiga ℓ1. Töös käsitletakse Banachi ruumide ümbernormeerimisi nii, et need sisaldavad Daugaveti või Delta-punkte. Selle tulemusena näidatakse, et klassikalised Banachi ruumid ℓp, kus pϵ[1,∞), on ümbernormeeritavad nii, et need sisaldavad Daugaveti punkte. See annab esimesed näited refleksiivsetest ruumidest, mis sisaldavad Daugaveti punkte. Lõpuks tuuakse välja mitmeid Banachi ruumide klasse, mis ei saa Daugaveti või Delta-punkte sisaldada.Daugavet and Delta-points were introduced as pointwise versions of the Daugavet property and the diametral local diameter-two property, respectively. Both of these properties belong to the class of diameter-two properties, meaning that every slice of the unit ball has diameter 2. In contrast, the mere existence of Daugavet or Delta-points does not imply such strong global properties. Indeed, there exist Banach spaces that contain Daugavet or Delta-points, but also admit slices of the unit ball with arbitrarily small diameter. In this thesis, we study Daugavet and Delta-points in various classes of Banach spaces, among these Lipschitz-free spaces and their duals. We provide characterizations for certain subclasses of these spaces, including a complete characterization of Daugavet points in Lipschitz-free spaces. Furthermore, we present an example of a metric space whose Lipschitz-free space has the Radon—Nikodým property and a Daugavet point. We also show that this Lipschitz-free space is a dual space, isomorphic to ℓ1. The thesis further investigates renormings of Banach spaces that admit Daugavet or Delta-points. As a result, we show that the classical spaces ℓp for pϵ[1,∞) can be renormed to contain a Daugavet point. This provides the first examples of reflexive spaces admitting Daugavet points. Finally, we introduce several classes of Banach spaces that cannot contain Daugavet or Delta-points.","abstract_has_math":false,"creators":["Veeorg, Triinu"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-29","date_published":"2025-08-29","updated_at":"2026-07-24T06:23:59Z","subjects":["doktoritööd"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10062/115534"],"render_values":[{"text":"hdl:10062/115534","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-08-29"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["doktoritööd"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10062/115534"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Daugaveti ja Delta-punktid on vastavalt Banachi ruumi Daugaveti omaduse ja diametraalse lokaalse diameeter-kahe omaduse punktilised versioonid. Mõlemad ruumide omadused kuuluvad diameeter-kaks omaduste klassi, mis tähendab, et iga ühikkera viilu diameeter on 2. Seevastu Daugaveti või Delta-punktide olemasolu ei nõua nii tugevaid globaalseid omadusi. Tõepoolest, leidub Banachi ruume, mis sisaldavad Daugaveti või Delta-punkte, kuid mille ühikkera viilud võivad olla kuitahes väikese diameetriga. Käesolevas väitekirjas uuritakse Daugaveti ja Delta-punkte erinevates Banachi ruumide klassides, sealhulgas Lipschitzi-vabades ruumides ja nende kaasruumides. Antakse iseloomustavad kriteeriumid nende ruumide teatud alamklassides, sealhulgas antakse Daugavet punktidele täielik kirjeldus kõigis Lipschitzi-vabades ruumides. Lisaks tuuakse näide meetrilisest ruumist, mille Lipschitzi-vaba ruum on Radon-Nikodými omadusega ning sisaldab ka Daugaveti punkti. Samuti näidatakse, et see Lipschitzi-vaba ruum on kaasruum, mis on isomorfne Banachi ruumiga ℓ1. Töös käsitletakse Banachi ruumide ümbernormeerimisi nii, et need sisaldavad Daugaveti või Delta-punkte. Selle tulemusena näidatakse, et klassikalised Banachi ruumid ℓp, kus pϵ[1,∞), on ümbernormeeritavad nii, et need sisaldavad Daugaveti punkte. See annab esimesed näited refleksiivsetest ruumidest, mis sisaldavad Daugaveti punkte. Lõpuks tuuakse välja mitmeid Banachi ruumide klasse, mis ei saa Daugaveti või Delta-punkte sisaldada.Daugavet and Delta-points were introduced as pointwise versions of the Daugavet property and the diametral local diameter-two property, respectively. Both of these properties belong to the class of diameter-two properties, meaning that every slice of the unit ball has diameter 2. In contrast, the mere existence of Daugavet or Delta-points does not imply such strong global properties. Indeed, there exist Banach spaces that contain Daugavet or Delta-points, but also admit slices of the unit ball with arbitrarily small diameter. In this thesis, we study Daugavet and Delta-points in various classes of Banach spaces, among these Lipschitz-free spaces and their duals. We provide characterizations for certain subclasses of these spaces, including a complete characterization of Daugavet points in Lipschitz-free spaces. Furthermore, we present an example of a metric space whose Lipschitz-free space has the Radon—Nikodým property and a Daugavet point. We also show that this Lipschitz-free space is a dual space, isomorphic to ℓ1. The thesis further investigates renormings of Banach spaces that admit Daugavet or Delta-points. As a result, we show that the classical spaces ℓp for pϵ[1,∞) can be renormed to contain a Daugavet point. This provides the first examples of reflexive spaces admitting Daugavet points. Finally, we introduce several classes of Banach spaces that cannot contain Daugavet or Delta-points."]},{"key":"dc:title","label":"Title","values":["Daugavet and Delta-points in Banach spaces: Lipschitz-free spaces, their duals, and renormings"]}]}],"canonical_facts":{"dc:date.issued":["2025-08-29"],"dc:description.other":["Daugaveti ja Delta-punktid on vastavalt Banachi ruumi Daugaveti omaduse ja diametraalse lokaalse diameeter-kahe omaduse punktilised versioonid. Mõlemad ruumide omadused kuuluvad diameeter-kaks omaduste klassi, mis tähendab, et iga ühikkera viilu diameeter on 2. Seevastu Daugaveti või Delta-punktide olemasolu ei nõua nii tugevaid globaalseid omadusi. Tõepoolest, leidub Banachi ruume, mis sisaldavad Daugaveti või Delta-punkte, kuid mille ühikkera viilud võivad olla kuitahes väikese diameetriga. Käesolevas väitekirjas uuritakse Daugaveti ja Delta-punkte erinevates Banachi ruumide klassides, sealhulgas Lipschitzi-vabades ruumides ja nende kaasruumides. Antakse iseloomustavad kriteeriumid nende ruumide teatud alamklassides, sealhulgas antakse Daugavet punktidele täielik kirjeldus kõigis Lipschitzi-vabades ruumides. Lisaks tuuakse näide meetrilisest ruumist, mille Lipschitzi-vaba ruum on Radon-Nikodými omadusega ning sisaldab ka Daugaveti punkti. Samuti näidatakse, et see Lipschitzi-vaba ruum on kaasruum, mis on isomorfne Banachi ruumiga ℓ1. Töös käsitletakse Banachi ruumide ümbernormeerimisi nii, et need sisaldavad Daugaveti või Delta-punkte. Selle tulemusena näidatakse, et klassikalised Banachi ruumid ℓp, kus pϵ[1,∞), on ümbernormeeritavad nii, et need sisaldavad Daugaveti punkte. See annab esimesed näited refleksiivsetest ruumidest, mis sisaldavad Daugaveti punkte. Lõpuks tuuakse välja mitmeid Banachi ruumide klasse, mis ei saa Daugaveti või Delta-punkte sisaldada.Daugavet and Delta-points were introduced as pointwise versions of the Daugavet property and the diametral local diameter-two property, respectively. Both of these properties belong to the class of diameter-two properties, meaning that every slice of the unit ball has diameter 2. In contrast, the mere existence of Daugavet or Delta-points does not imply such strong global properties. Indeed, there exist Banach spaces that contain Daugavet or Delta-points, but also admit slices of the unit ball with arbitrarily small diameter. In this thesis, we study Daugavet and Delta-points in various classes of Banach spaces, among these Lipschitz-free spaces and their duals. We provide characterizations for certain subclasses of these spaces, including a complete characterization of Daugavet points in Lipschitz-free spaces. Furthermore, we present an example of a metric space whose Lipschitz-free space has the Radon—Nikodým property and a Daugavet point. We also show that this Lipschitz-free space is a dual space, isomorphic to ℓ1. The thesis further investigates renormings of Banach spaces that admit Daugavet or Delta-points. As a result, we show that the classical spaces ℓp for pϵ[1,∞) can be renormed to contain a Daugavet point. This provides the first examples of reflexive spaces admitting Daugavet points. Finally, we introduce several classes of Banach spaces that cannot contain Daugavet or Delta-points."],"dc:identifier":["hdl:10062/115534"],"dc:subject":["doktoritööd"],"dc:title":["Daugavet and Delta-points in Banach spaces: Lipschitz-free spaces, their duals, and renormings"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T06:23:59Z"}