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Reflexivity and nonweakly null maximizing sequences


Authors: Richard M. Aron, Domingo García, Daniel Pellegrino and Eduardo V. Teixeira
Journal: Proc. Amer. Math. Soc. 148 (2020), 741-750
MSC (2010): Primary 46B20; Secondary 46B25, 46G25
DOI: https://doi.org/10.1090/proc/14728
Published electronically: August 7, 2019
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Abstract: We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize norm attaining scalar-valued continuous $ 2$-homogeneous polynomials on $ \ell _{2}$.


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Additional Information

Richard M. Aron
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email: aron@math.kent.edu

Domingo García
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain
Email: domingo.garcia@uv.es

Daniel Pellegrino
Affiliation: Departamento de Matemática, UFPB, João Pessoa, PB, Brazil
Email: dmpellegrino@gmail.com

Eduardo V. Teixeira
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: Eduardo.Teixeira@ucf.edu

DOI: https://doi.org/10.1090/proc/14728
Keywords: Maximizing sequence, norm attaining, Banach space
Received by editor(s): February 25, 2019
Received by editor(s) in revised form: June 3, 2019
Published electronically: August 7, 2019
Additional Notes: The first and second authors were supported by MINECO and FEDER project MTM2017-83262-C2-1-P
The second author was also supported by PROMETEO/2017/102 of the Generalitat Valenciana
The third author was supported by CNPq-Grant 307327/2017-5
The fourth author was supported by FUNCAP/CNPq/PRONEX Grant 00068.01.00/15
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2019 American Mathematical Society