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Daugaveti ja Delta punktid Banachi ruumides: Lipschitzi-vabades ruumides, nende kaasruumides ja ümbernormeeringutes
Get PDFDaugaveti 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.https://www.ester.ee/record=b576047
Daugavet- and Delta-points in spaces of Lipschitz functions
Get PDFA norm one element of a Banach space is a Daugavet-point (respectively,~a
-point) if every slice of the unit ball (respectively,~every slice of
the unit ball containing ) contains an element that is almost at distance 2
from . We prove the equivalence of Daugavet- and -points in spaces
of Lipschitz functions over proper metric spaces and provide two
characterizations for them. Furthermore, we show that in some spaces of
Lipschitz functions, there exist -points that are not Daugavet-points.
Lastly, we prove that every space of Lipschitz functions over an infinite
metric space contains a -point but might not contain any
Daugavet-points
Delta- ja Daugaveti-punktid Banachi ruumide otsesummades
Get PDFBakalaurusetöös selgitatakse välja Banachi ruumide summaruumide ja nende liidetavate nii Daugaveti-punktide kui ∆-punktide olemasolu vaheline seos ning nende punktide kuju summaruumides. Töö on terviklik teoreetiline uurimus, mis jätkab ja täiendab T. A. Abrahamseni, R. Halleri, V. Lima ja K. Pirki ühisartikli „Delta- and Daugavet-points in Banach spaces“ (arXiv:1812.02450 [math.FA]) tulemusi ning annab vastuse kahele seal püstitatud küsimusele
A note on Delta-points in Lipschitz-free spaces
Get PDFA norm one element x of a Banach space is a Daugavet-point (respectively, a Δ-point) if every slice of the unit ball (respectively, every slice of the unit ball containing x) contains an element that is almost at distance 2 from x. It is known that any finitely supported element μ in the unit sphere of a Lipschitz-free space ℱ (M) is a Δ-point if and only if for every ε > 0 and a slice S of Bℱ(M) with μ ∈ Sℱ(M) there exist u, v ∈ M with u ≠ v such that muv ∈ S and d(u,v) < ε. The aim of this note is to show that this characterization can also be applied to certain convex series of molecules
Daugavet- and Delta-points in Lipschitz-free Banach Spaces
Get PDFMagistritöös esitatakse kriteeriumid Daugaveti- ja Delta-punktide kirjeldamiseks Lipschitzi-vabades Banachi ruumides. Saadud tulemused täiendavad M. Jung ja A. Rueda Zoca hiljutises eeltrükis "Daugavet points and ∆-points in Lipschitz-free Banach spaces" avaldatud tulemusi.In this thesis, we characterize Daugavet- and Delta-points in Lipschitz-free Banach spaces. Our results complement the ones in the recent preprint "Daugavet points and ∆-points in Lipschitz-free Banach spaces" by M. Jung and A. Rueda Zoca
Weakly almost square Lipschitz-free spaces
Get PDFWe construct a Lipschitz-free space that is locally almost square but not
weakly almost square; this is the first example of such a Banach space. We also
prove a result, which indicates that geodesic metric spaces are a potential
metric characterization for weakly almost square Lipschitz-free spaces. Lastly,
we prove that a Lipschitz-free space can not have the symmetric strong diameter
property
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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