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1. Brito, Leonardo da Silva. Versões das propriedades A e B de Lindenstrauss para operadores compactos.

Degree: 2018, Universidade Federal do Amazonas

URL: https://tede.ufam.edu.br/handle/tede/6386 

O objetivo desta dissertação é estudar as versões das propriedades A e B de Lindenstrauss para operadores compactos. No decorrer do nosso trabalho, apresentamos resultados sobre a topologia fraca-estrela, bases de Schauder, propriedades da aproximação, espaços de Banach cuja norma depende localmente de finitas coordenados, espaço estritamente convexo, espaço uniformemente convexo, dentre outros. Em 2014 Miguel Martín publicou um artigo respondendo de maneira positiva a seguinte pergunta: Existem operadores compactos entre espaços de Banach que não podem ser aproximados por operadores compactos que atingem a norma? Ao fazer isso, introduziu, no mesmo trabalho, duas propriedades chamadas de propriedades Ak e Bk ou versões para operadores compactos das propriedades de Lindenstrauss. Nesta dissertação, são apresentados de maneira detalhada resultados relacionados às propriedades A e B de Lindenstrauss e propriedades Ak e Bk.

The main goal in this dissertation is to study the versions for compact operators of Lindenstrauss property A and B. In the course of our work, we present results concerning weak-star topology, Schauder basis, approximation properties, Banach spaces that locally depend upon finitely many coordinates, strictly convex spaces, uniformly convex spaces, among others. In 2014 Miguel Martín answered positively the following question: Are there compact operators between Banach spaces that can not be approximated by compact operators that attain their norms? In order to do that, he introduced two properties called properties Ak and Bk or versions for compact operators of Lindenstrauss properties. In this dissertation we present some results regarding Lindenstrauss properties A and B, and we also provide several results regarding properties Ak and Bk.

CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico

Advisors/Committee Members: Alves, Thiago Rodrigo, 98547607153, http://lattes.cnpq.br/4049150059686360, Alves, Thiago Rodrigo, Botelho, Geraldo Márcio de Azevedo, Jacinto, Flávia Morgana de Oliveira, [email protected].

Subjects/Keywords: Operador compacto; Propriedades de Lindenstrauss; Propriedade da aproximação; Espaços uniformemente convexos; Compact operator; Lindenstrauss properties; Approximation properties; Uniformly convex space; CIÊNCIAS EXATAS E DA TERRA: MATEMÁTICA

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Brito, L. d. S. (2018). Versões das propriedades A e B de Lindenstrauss para operadores compactos. (Masters Thesis). Universidade Federal do Amazonas. Retrieved from https://tede.ufam.edu.br/handle/tede/6386

Chicago Manual of Style (16th Edition):

Brito, Leonardo da Silva. “Versões das propriedades A e B de Lindenstrauss para operadores compactos.” 2018. Masters Thesis, Universidade Federal do Amazonas. Accessed February 27, 2021. https://tede.ufam.edu.br/handle/tede/6386.

MLA Handbook (7th Edition):

Brito, Leonardo da Silva. “Versões das propriedades A e B de Lindenstrauss para operadores compactos.” 2018. Web. 27 Feb 2021.

Vancouver:

Brito LdS. Versões das propriedades A e B de Lindenstrauss para operadores compactos. [Internet] [Masters thesis]. Universidade Federal do Amazonas; 2018. [cited 2021 Feb 27]. Available from: https://tede.ufam.edu.br/handle/tede/6386.

Council of Science Editors:

Brito LdS. Versões das propriedades A e B de Lindenstrauss para operadores compactos. [Masters Thesis]. Universidade Federal do Amazonas; 2018. Available from: https://tede.ufam.edu.br/handle/tede/6386


University of North Texas

2. Farmer, Matthew Ray. Applications in Fixed Point Theory.

Degree: 2005, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc4971/ 

Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces. Advisors/Committee Members: Bator, Elizabeth M., Lewis, Paul, Jackson, Stephen C..

Subjects/Keywords: Fixed point theory.; Banach spaces.; metric space; Banach spaces; non-expansive maps; contraction maps; fixed points; uniformly convex Banach spaces

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Farmer, M. R. (2005). Applications in Fixed Point Theory. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc4971/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Farmer, Matthew Ray. “Applications in Fixed Point Theory.” 2005. Thesis, University of North Texas. Accessed February 27, 2021. https://digital.library.unt.edu/ark:/67531/metadc4971/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Farmer, Matthew Ray. “Applications in Fixed Point Theory.” 2005. Web. 27 Feb 2021.

Vancouver:

Farmer MR. Applications in Fixed Point Theory. [Internet] [Thesis]. University of North Texas; 2005. [cited 2021 Feb 27]. Available from: https://digital.library.unt.edu/ark:/67531/metadc4971/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Farmer MR. Applications in Fixed Point Theory. [Thesis]. University of North Texas; 2005. Available from: https://digital.library.unt.edu/ark:/67531/metadc4971/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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