On Locally Uniformly Rotund Renormings in C(K) Spaces

2010 ◽  
Vol 62 (3) ◽  
pp. 595-613 ◽  
Author(s):  
J. F. Martínez ◽  
A. Moltó ◽  
J. Orihuela ◽  
S. Troyanski
Keyword(s):  
Banach Spaces ◽  
Ad Hoc ◽  
Rotund Norm

AbstractA characterization of the Banach spaces of type C(K) that admit an equivalent locally uniformly rotund norm is obtained, and a method to apply it to concrete spaces is developed. As an application the existence of such renorming is deduced when K is a Namioka–Phelps compact or for some particular class of Rosenthal compacta, results which were originally proved with ad hoc methods.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1827
Author(s):  
Pablo Manuel Berná ◽  
Diego Mondéjar
Keyword(s):  
Banach Spaces ◽  
Functional Characterization

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco.

scholarly journals Sets of periods for chaotic linear operators

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. A. Conejero ◽  
F. Martínez-Giménez ◽  
A. Peris ◽  
F. Rodenas
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

scholarly journals Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

Positivity ◽  
2012 ◽  
Vol 17 (3) ◽  
pp. 535-587
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Banach Spaces ◽  
Bmo Functions ◽  
Umd Banach Spaces

scholarly journals From raw reads to trees: Whole genome SNP phylogenetics across the tree of life

2015 ◽  
Author(s):  
Sanaa Afroz Ahmed ◽  
Chien-Chi Lo ◽  
Po-E Li ◽  
Karen W Davenport ◽  
Patrick S.G. Chain
Keyword(s):  
Ad Hoc ◽  
Phylogenetic Reconstruction ◽  
Clinical Samples ◽  
Nucleotide Polymorphisms ◽  
Single Nucleotide ◽  
Complex Samples ◽  
Phylogenetic Characterization ◽  
Genome Wide ◽  
Genome Assemblies

Next-generation sequencing is increasingly being used to examine closely related organisms. However, while genome-wide single nucleotide polymorphisms (SNPs) provide an excellent resource for phylogenetic reconstruction, to date evolutionary analyses have been performed using different ad hoc methods that are not often widely applicable across different projects. To facilitate the construction of robust phylogenies, we have developed a method for genome-wide identification/characterization of SNPs from sequencing reads and genome assemblies. Our phylogenetic and molecular evolutionary (PhaME) analysis software is unique in its ability to take reads and draft/complete genome(s) as input, derive core genome alignments, identify SNPs, construct phylogenies and perform evolutionary analyses. Several examples using genomes and read datasets for bacterial, eukaryotic and viral linages demonstrate the broad and robust functionality of PhaME. Furthermore, the ability to incorporate raw metagenomic reads from clinical samples with suspected infectious agents shows promise for the rapid phylogenetic characterization of pathogens within complex samples.

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