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THE HAHN-BANACH THEOREM AND SOLUTION OF RELATED PROBLEMSNguyen, Fonzie T 01 December 2014 (has links)
We give an overview of Hahn-Banch Theorems. We present the statements of these theorems along with some definitions that are required to understand these statements and work out some applications.
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Análise funcional : um texto para iniciação científica /Antonow, Liliane Martinez. January 2011 (has links)
Orientador: Simone Mazzini Bruschi / Banca: Ricardo Pereira da Silva / Banca: Vera Lúcia Carbone / Resumo: Este trabalho consistiu em coletar e desenvolver uma sequência didática para o ensino de Análise Funcional aos estudantes de iniciação científica. Neste sentido a dissertação foi escrita para ser utilizada como livro-texto, transmitindo uma introdução de Análise Funcional e com o objetivo que ao final os estudantes estejam aptos a estudar textos mais específicos / Abstract: This work suggests a didatic road map for teaching Functional Analysis to un- dergraduated students who wish to initiate a scientific carrier. The dissertation was written an introductory text book of Functional Analysis ofter which students could migrate to more specific papers / Mestre
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Duals and Reflexivity of Certain Banach SpacesDahler, Cheryl L. (Cheryl Lewis) 08 1900 (has links)
The purpose of this paper is to explore certain properties of Banach spaces. The first chapter begins with basic definitions, includes examples of Banach spaces, and concludes with some properties of continuous linear functionals. In the second chapter, dimension is discussed; then one version of the Hahn-Banach Theorem is presented. The third chapter focuses on dual spaces and includes an example using co, RI, and e'. The role of locally convex spaces is also explored in this chapter. In the fourth chapter, several more theorems concerning dual spaces and related topologies are presented. The final chapter focuses on reflexive spaces. In the main theorem, the relation between compactness and reflexivity is examined. The paper concludes with an example of a non-reflexive space.
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Análise funcional: um texto para iniciação científicaAntonow, Liliane Martinez [UNESP] 28 July 2011 (has links) (PDF)
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antonow_lm_me_rcla.pdf: 366751 bytes, checksum: adcb2380c3d0056c89dc0a6656d12c25 (MD5) / Este trabalho consistiu em coletar e desenvolver uma sequência didática para o ensino de Análise Funcional aos estudantes de iniciação científica. Neste sentido a dissertação foi escrita para ser utilizada como livro-texto, transmitindo uma introdução de Análise Funcional e com o objetivo que ao final os estudantes estejam aptos a estudar textos mais específicos / This work suggests a didatic road map for teaching Functional Analysis to un- dergraduated students who wish to initiate a scientific carrier. The dissertation was written an introductory text book of Functional Analysis ofter which students could migrate to more specific papers
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Espaços Vetoriais TopológicosCavalcante, Wasthenny Vasconcelos 27 February 2015 (has links)
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Previous issue date: 2015-02-27 / In this work we investigate the concept of topological vector spaces and their properties.
In the rst chapter we present two sections of basic results and in the other
sections we present a more general study of such spaces. In the second chapter we
restrict ourselves to the real scalar eld and we study, in the context of locally convex
spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak,
weak-star, of bounded convergence and of pointwise convergence topologies. Finally
we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and
the Closed Graph Theorem. / Neste trabalho, estudamos o conceito de espa cos vetoriais topol ogicos e suas propriedades.
No primeiro cap tulo, apresentamos duas se c~oes de resultados b asicos e,
nas demais se c~oes, apresentamos um estudo sobre tais espa cos de forma mais ampla.
No segundo cap tulo, restringimo-nos ao corpo dos reais e fazemos um estudo sobre
os espa cos localmente convexos, o Teorema de Hahn-Banach, o Teorema de Banach-
Alaoglu, constru mos as topologias fraca, fraca-estrela, da converg^encia limitada e da
converg^encia pontual. Por ultimo, estudamos o Teorema da Limita c~ao Uniforme, o Teorema
do Gr a co Fechado e o da Aplica c~ao Aberta no contexto mais geral dos espa cos
de Fr echet.
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