No description available.

No description available.

No description available.

Hemos de considerar la estructura de multiplicadores y derivaciones en álgebras de operadores. En procura de que el trabajo no se diluya en especificaciones técnicas tratamos en todo caso de situarlo en el contexto general de la teoría de derivaciones en álgebras de Banach. Por ello se citará frecuentemente [35], trabajo que adjuntamos a esta tesis, en el Anexo I. Asimismo, en varias de las secciones de este documento daré los elementos mínimos que permítan al lector una mejor comprensión de los temas abordados. El trabajo está dividido en cuatro capítulos principales, a saber: el Capítulo 1 de carácter introductorio, el Capítulo 2 acerca derivaciones en álgebras nucleares, el Capítulo 3 acerca de B-derivaciones, y el Capítulo 4 sobre ( ; )-derivaciones. Los resultados principales del Capítulo 2, publicados en [36], están en la Sección 2.6. La entidad de este estudio reside en el Teorema 2.5.2, que precisa condiciones fuertemente restrictivas de amenabilidad o super-amenabilidad de álgebras nucleares construídas sobre pares duales de espacios de Banach. Estudiamos entonces la estructura de las derivaciones de tipo Hadamard cuyos resultados principales son Lema 2.6.10, Prop. 2.6.11, Prop. 2.6.12, Prop. 2.6.14, Prop. 2.6.15 y Teo. 2.6.13. Los resultados principales del Capítulo 3, publicados en [38], los tenemos en las Secciones 3.2 y 3.3. Consideramos un teorema de estructura y y la descripción exhaustiva de B- derivaciones sobre l1 (N) en la forma de los teoremas 3.2.1, 3.3.1 y el Corolario 3.3.2. En el Capítulo 4 consideraré dos problemas enunciados por M. Mirzavaziri (cf. [40], 2009) acerca de estructura de ( ; )-derivaciones. La investigación, de carácter algebraica, pudo hacerse en un marco elemental finito-dimensional. Los resultados principales, pu-blicados en [37], los tenemos en los teoremas 4.2.2, 4.2.3 y 4.2.5. / We consider the structure of multipliers and derivations in operator algebras. In order to avoid a lot of technical specifications and for the sake of clearness we try to put our matter in the general framework of the theory of derivations on Banach algebras. So, I added my undergraduated thesis [35], in the Appendix I, where various aspects of the theory are treated more exhaustively. The work is divided into four main chapters; the Chapter 1 by way of introduction, the Chapter 2 about derivations in nuclear algebras, the Chapter 3 about B-derivations and the Chapter 4 about ( ; )-derivations. The main results of Chapter 2, published in [36], are in Section 2.6. The importance of this study lies in Theorem 2.5.2, that requires highly restrictive conditions of amenabilithy or super-amenabilithy of nuclear algebras built on dual pairs of Banach spaces. Then studied the structure of derivations type Hadamard (Lemma 2.6.10, Prop. 2.6.11, Prop. 2.6.12, Prop. 2.6.14, Prop. 2.6.15 and Teo. 2.6.13). The main results of Chapter 3, published in [38], we have them in Sections 3.2 and 3.3. We consider a structure theorem and the comprehensive description of B--derivations on l1 (N) in the form of Theorems 3.2.1, 3.3.1 and the Corollary 3.3.2. In Chapter 4 solve two problems stated by M. Mirzavaziri (cf. [40], 2009) about the structure of ( ; )-derivations. The research, algebraic in nature, could be done in a basic finitedimensional framework. The main results, reported in [37], are in the Theorems 4.2.2, 4.2.3 and

Sin excepción, en este trabajo U denota un álgebra de Banach compleja. Los aportes originales de este trabajo se dan en tres capítulos: - En el Capítulo 2 asumimos que el álgebra de Banach U es Arens regular y consideramos derivaciones acotadas D : U→U* : Como U** admíte una estructura natural de álgebra de Banach estudiamos problemas concernientes a cuándo el operador adjunto D* : U** → U* es derivación. En particular, analizaremos el caso de la clase D(U) de derivaciones tales que (a,D(a)) = 0 para todo E U, las que caracterizamos. Veremos que para que el álgebra U sea débilmente amenable es necesario y suficiente que D(U) sea no trivial. Analizamos esta problemática en el caso específico de álgebras de Beurling construídas sobre el grupo aditivo de los enteros. Esta investigación está publicada en el New York Journal of Matematics [1]. - En el Capítulo 3 nos damos a la tarea de caracterizar los elementos a** E U** para los que a**U* es débil*-cerrado. Esta investigación tiene relación con la existencia de aproximaciones acotadas de la identidad en ideales cerrados del álgebra, por lo que se trata de un tema que requiere atención. El material presentado está en etapa de prensa de las Actas del XIV Congreso Dr. A. Monteiro [2]. - En el Capítulo 4 retomamos el tema derivaciones, ahora sobre el álgebra de convolución asociada a permutaciones de un conjunto numerable en si mismo. Es profusa la literatura sobre el particular, y naturalmente se da la necesidad de estudiar álgebras de convolución nito-dimensionales. Veremos cómo las algebras de convolución sobre grupos nitos de permutaciones pueden ser inmersas en álgebras de matrices. Por otra parte, si bien toda derivación centralizante sobre un álgebra de Banach mapea sobre el radical se verá que esta condición no es necesaria, incluso en el contexto finito dimensional. Esta investigación está en prensa en Acta Mathematica Academiae Paedagogicae Nyíregyháziensis [3]. / Without exception, U will denote a complex Banach algebra. Our original contributions in this work are given in three chapters: - In Chapter 2 we assume that the Banach algebra U is Arens regular and we consider bounded derivations D : U→U* : As U** has a natural structure of a Banach algebra we seek on conditions under which the adjoint operator D* : U** U→U* is a derivation. We shall characterize the class D(U) of bounded derivations so that (a,D(a)) = 0 for all a E U. We shall prove that the Banach algebra U is weakly amenable if and only if D(U) is non trivial. We shall consider this matters in the speci c case of Beurling algebras constructed on the additive group of integers. This research was published in the New York Journal of Mathematics [1]. - In Chapter 3 we shall characterize the elements a** E U** so that a**U* is weak*- closed. This investigation is connected with the existence of bounded approximate identities within closed ideals of U and is a matter that deserves attention. This investigation is in press of Actas del XIV Congreso Dr. A. Monteiro [2]. - In Chapter 4 we return to the issue of derivations, now on the convolution algebra on the discrete permutation group on a countable set. There is a huge literature in this matter and it is necessary to study nite dimensional convolution algebras. Althought any central derivation maps on the radical we shall see that this condition is not necessary, event in the nite dimensional context. This investigation is in press of Acta Mathematica Academiae Paedagogicae Nyíregyháziensis [3]. / TEXTO PARCIAL en período de teletrabajo

Let G be a reductive group, and P a parabolic subgroup. Let L ⊆ K be finiteextensions of Qp and let G = G(L), P = P(L). In this thesis, we define the Iwasawa algebra K[[G]] and prove that it is isomorphic to the convolution algebra of compactly supported distributions on G. We show that under Schneider-Teitelbaum duality the func- tor of parabolic induction on the side of the admissible representations corresponds to the functor K[[G]] ⊗K[[P ]] − on the side of the K[[G]]-modules.This has important applications in the theory of admissible representations of G on p-adicBanach spaces. In particular, we prove the parabolic induction of an admissible represen- tation is again admissible, and prove Frobenius reciprocity for admissible representations.

For decades, mathematical games have been used to explore various properties of particular sets. The Banach-Mazur game is the prototypical intersection game and its modifications by e.g., W. Schmidt and C. McMullen are used in number theory and many other areas of mathematics. We give a brief survey of a few of these modifications and their properties followed by our own modification. One of our main results is proving that this modification is equivalent to an important set theoretic game, called the perfect set game, developed by M. Davis.

.

Neste trabalho aplicamos técnicas de combinatória infinitária e forcing na teoria dos espaços de Banach, investigando propriedades dos espaços de Banach da forma C(K), formado pelas funções reais contínuas sobre K com a norma do supremo, com poucos operadores, no sentido de que todo operador em C(K) é da forma gI+S, onde I é o operador identidade, g pertence a C(K) e S é fracamente compacto. Enfatizamos as construções onde K é conexo, o que implica que C(K) é indecomponível. Assumindo Axioma Diamante, um axioma combinatório mais forte que a Hipótese do Contínuo, construímos um espaço de Banach C(K) tal que C(L) tem poucos operadores, para todo L subespaço fechado de K. Sob a Hipótese do Contínuo construímos um espaço C(K) indecomponível com poucos operadores tal que K contém $\\beta N$ homeomorficamente. Em ZFC construímos um espaço C(K) com poucos operadores em um sentido estritamente mais fraco. Também mostramos a existência de pelo menos contínuo espaços de Banach C(K) indecomponíveis dois a dois essencialmente incomparáveis. Usando forcing provamos que existe consistentemente um espaço de Banach C(K) de densidade menor que contínuo com poucos operadores e um C(K) indecomponível de densidade menor que contínuo. / In this work we apply techniques of infinitary combinatorics and forcing in Banach spaces theory, investigating the compact topological spaces K such that the Banach space C(K), consisting of the continuous real-valued functions on K with the supremum norm, has few operators, in the sense that all operators on C(K) have the form gI+S, where I is the identity operator, g\\ belongs to C(K) and S is weakly compact. We emphasize the constructions where K is connected, which implies that C(K) is indecomposable. Assuming Diamond Axiom, a combinatoric axiom stronger than the continuum hypothesis, we construct a Banach space C(K) where C(L) has few operators, for every L closed subspace of K. Under continuum hypothesis we construct an indecomposable C(K) with few operators such that K contains $\\beta \\mathbb$ homeomorphically. In ZFC we construct a space C(K) with few operators in a strictly weaker sense. We also show the existence of at least continuum pairwise essentially incomparable indecomposable Banach spaces C(K). Using forcing, we prove that there exists consistently a Banach space C(K) of density smaller than continuum having few operators and an indecomposable C(K) of density smaller than continuum.

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-07-28Bitstream added on 2014-06-13T20:16:06Z : No. of bitstreams: 1 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