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Journal of Functional Analysis, ISSN 0022-1236, 05/2019, Volume 276, Issue 10, pp. 3226 - 3260
Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on c0(Γ) can be approximated uniformly on bounded sets by polyhedral... 
Renorming | Polyhedrality | Approximation | Smoothness | MATHEMATICS | POLYHEDRAL APPROXIMATION | SMOOTH APPROXIMATIONS
Journal Article
Canadian Mathematical Bulletin, ISSN 0008-4395, 09/2018, Volume 61, Issue 3, pp. 449 - 457
We show that if x is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good... 
Unconditional compact approximation property | Denting point | Strongly extreme point | MATHEMATICS | unconditional compact approximation property | denting point | strongly extreme point | Mathematics - Functional Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 84 - 92
A sequence in a separable Banach space X 〈resp. in the dual space X⁎〉 is said to be overcomplete (OC in short) 〈resp. overtotal (OT in short) on X〉 whenever... 
Almost overcomplete sequence | Almost overtotal sequence | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
QUARTERLY JOURNAL OF MATHEMATICS, ISSN 0033-5606, 06/2019, Volume 70, Issue 2, pp. 409 - 427
The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder... 
MATHEMATICS | SMOOTH | APPROXIMATION | NORMS
Journal Article
Milan Journal of Mathematics, ISSN 1424-9286, 12/2016, Volume 84, Issue 2, pp. 231 - 242
We study smoothness and strict convexity of (the bidual) of Banach spaces in the presence of diameter 2 properties.We prove that the strong diameter 2 property... 
Diameter 2 property | 46B04 | Analysis | 46B20 | Mathematics, general | Mathematics | strictly convex norm | Daugavet property | smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | Resveratrol
Journal Article
Studia Mathematica, ISSN 0039-3223, 2016, Volume 232, Issue 3, pp. 227 - 242
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of C[0, 1] with the diameter 2 property (D2P), i.e. every non-empty relatively... 
Diameter 2 property | Midpoint locally uniformly rotund | Daugavet property | MATHEMATICS | diameter 2 property | WEAKLY OPEN SUBSETS | SLICES | midpoint locally uniformly rotund | BANACH-SPACES | M-IDEALS
Journal Article
04/2020
We prove that a Banach space of continuous functions $C(K)$ has a renorming that is uniformly rotund in every direction (URED) if and only if the compact space... 
Mathematics - Functional Analysis
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 1/2012, Volume 104, Issue 1, pp. 197 - 222
We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with G -diagonals and Gruenhage... 
MATHEMATICS | ROTUND NORMS | GULKO | TREES | DEVILLES MASTER LEMMA | BANACH-SPACES | RENORMING THEORY | DESCRIPTIVE COMPACT SPACES | C(K) SPACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2020, Volume 487, Issue 2, p. 124003
We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on... 
Almost square Banach space | Octahedral Banach space | M-ideal | Locally almost square Banach space | Intersection property | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Set-Valued and Variational Analysis, ISSN 1877-0533, 12/2013, Volume 21, Issue 4, pp. 649 - 659
Some new classes of compacta K are considered for which C(K) endowed with the pointwise topology has a countable cover by sets of small local norm-diameter. 
Geometry | Pointwise SLD | Distributive lattice | 46B26 | Analysis | Compact semilattice | Mathematics | Space of continuous functions | 03G10 | MATHEMATICS, APPLIED | SETS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2009, Volume 41, Issue 5, pp. 831 - 840
We present equivalent conditions for a space X with an unconditional basis to admit an equivalent norm with a strictly convex dual norm. 
MATHEMATICS | DESCRIPTIVE COMPACT SPACES | BANACH-SPACES | NORMS
Journal Article
12/2019
We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on... 
Mathematics - Functional Analysis
Journal Article
04/2018
Relatively recently it was proved that if $\Gamma$ is an arbitrary set, then any equivalent norm on $c_0(\Gamma)$ can be approximated uniformly on bounded sets... 
Mathematics - Functional Analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2006, Volume 237, Issue 2, pp. 373 - 390
An upper bound q ( c ) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity... 
Renorming | Moduli of convexity and smoothness | Banach space geometry | MATHEMATICS | renorming | moduli of convexity and smoothness | SERIES | INNER PRODUCT-SPACES | Universities and colleges
Journal Article
Topology and its Applications, ISSN 0166-8641, 04/2020, p. 107211
Journal Article
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, ISSN 1578-7303, 2009, Volume 103, Issue 1, pp. 75 - 85
A completely geometrical approach for the Construction of locally uniformly rotund norms and the associated networks on a normed space X is presented. A new... 
Slice localization | Completion | LUR renorming | Decomposition method | Network | MATHEMATICS | completion | decomposition method | LOCALLY UNIFORMLY CONVEX | BANACH-SPACES | NORMS | slice localization | network | Studies
Journal Article
04/2018
We show that, if $X$ is a closed subspace of a Banach space $E$ and $Z$ is a closed subspace of $E^*$ such that $Z$ is norming for $X$ and $X$ is total over... 
Mathematics - Functional Analysis
Journal Article
04/2018
The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder... 
Mathematics - Functional Analysis
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2012, Volume 104, Issue 1, pp. 197 - 222
We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with G delta -diagonals and... 
Equivalence | Axioms | Mathematical analysis | Norms | Topology | Banach space
Journal Article
06/2016
We study smoothness and strict convexity of (the bidual) of Banach spaces in the presence of diameter 2 properties. We prove that the strong diameter 2... 
Mathematics - Functional Analysis
Journal Article
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