Thesis (Ph. D.)--University of Wisconsin--Madison, 1951. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 46-47).

Let X be a Hausdorff locally convex space, U be a base for closed absolutely convex O-neighborhoods in X , K C X be nonempty. For each U є U , we denote by P[subscript u] the gauge of U. Then T : K ↦ K is said to be nonexpansive w.r.t. U if and only if for each U є U, P[subscript u](T(x) - T(y)) ≤ P[subscript u](x - y) for all x, y є K; T: K ↦ K is said to be strictly contractive w.r.t. U if and. only if for each U є U, there is a constant λ[subscript u] with 0 ≤ λ[subscript u] < 1 such that P[subscript u](T(x) - T(y)) ≤λ[subscript u]P[subscript u](x - y) for all x, y є K . The concept of nonexpansive (respectively strictly contractive) mappings is originally defined on a metric space. The above definitions are generalizations if the topology on X is induced by a translation invariant metric, and in particular if X is a normed space. An analogue of the Banach contraction mapping principle is proved and some examples together with an implicit function theorem are shown as applications. Moreover several fixed point theorems for various kinds of nonexpansive mappings are obtained. The convergence of nets of nonexpansive mappings and that of fixed points are also studied. Finally on sets with 'complete normal structure', a common fixed point theorem is obtained for an arbitrary family of 'commuting' nonexpansive mappings while on sets with 'normal structure', a common fixed point, theorem for an arbitrary family of (not necessarily commuting) 'weakly periodic' nonexpansive mappings is obtained. / Science, Faculty of / Mathematics, Department of / Graduate

by Ngai-ching Wong. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 197-201.

<p> The major results of this work include an isomorphism theorem for B-complete barrelled spaces with similar bases and a theorem which shows that the cone associated with a separating biorthogonal system in a perfect C.N.S. has a basis. We also obtain some applications of the former result in the case of dual generalized bases and some results concerning Schauder bases in countably barrelled spaces.</p> / Thesis / Doctor of Philosophy (PhD)

Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.

Song-Jian Han. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 72-73). / Acknowledgement --- p.i / Abstract --- p.ii / Introduction --- p.iii / Chapter 1 --- Topological Vector Spaces and Elemantary Duality Theory --- p.1 / Chapter 1.1 --- Locally Convex Spaces --- p.2 / Chapter 1.2 --- Bornological Spaces and Bornological Vector Spaces --- p.4 / Chapter 1.3 --- Elementary Properties of Dual Spaces --- p.6 / Chapter 1.4 --- Topological Injections and Surjections Bornological Injections and Surjections --- p.10 / Chapter 2 --- Locally Convex Riesz Spaces --- p.15 / Chapter 2.1 --- Ordered Vector Spaces --- p.15 / Chapter 2.2 --- Riesz Space --- p.18 / Chapter 2.3 --- Locally Convex Riesz Spaces --- p.20 / Chapter 3 --- Half-Full Injections and Half-Decomposable Surjections Half- Full Bornological Injections and Half-Decomposable Bornologi- cal Surjections --- p.24 / Chapter 4 --- Operator Modules between Locally Convex Riesz Spaces --- p.35 / Chapter 4.1 --- Preliminaries --- p.35 / Chapter 4.2 --- Operator Modules and Ideal Cones --- p.37 / Chapter 4.3 --- The Half-Full Injective Hull and the Half-Decomposable Bornolog- ical Surjective Hull of Operator Modules Between Locally Convex Riesz Spaces --- p.41 / Chapter 4.4 --- Extensions of Operator Modules and Ideal Cones --- p.57 / References --- p.72

<p> The closed graph and open mapping theorems are two of the deeper results in the theory of locally convex spaces. They are very rich in their applications in functional analysis. This thesis contains some extensions of these theorems in locally convex spaces. We begin with a study of α-spaces, and γ-spaces, which leads us naturally to a study of δ-spaces. On these spaces, we prove closed graph and open mapping theorems. Similar theorems are also proved for certain classes of Br ('&)-spaces. In particular, a closed graph theorem for B(m)-spaces enables us to characterise certain classes of B( &. y)-spaces. A consideration of countability conditions in locally convex spaces enables us to prove open mapping theorems in Br (J )-spaces. These theorems are then used to relate boundedness of linear mappings and their graphs. </p> / Thesis / Doctor of Philosophy (PhD)

This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p > 2 and addresses the problem of using that function to establish a relationship between the ordinary and the Sobolev gradients. The paper contains some numerical experiments and two computer codes.

Orientador: Mario Carvalho de Matos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T04:31:29Z (GMT). No. of bitstreams: 1 Favaro_ViniciusVieira_D.pdf: 758368 bytes, checksum: 1618ae17ed57109a9f307089c59fdbb6 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho introduzimos os espaços de funções (s , m (r , q))-somantes de um dado tipo e uma dada ordem, definidas em E, e os espaços de funções (s; (r; q))-quase-nucleares de um dado tipo e uma dada ordem, definidas em E, e provamos que a transformada de Fourier-Borel identica o dual do espaço de funções (s ; (r' , q'))-quase-nucleares de um dado tipo e uma dada ordem, definidas em E, com o espaço de funções (s';m (r' , q'))-somantes de um correspondente tipo e uma correspondente ordem, definidas em E'. Provamos também teoremas de divisão para funções (s ; m (r , q))-somantes de um dado tipo e uma dada ordem e teoremas de divisão envolvendo a transformada de Fourier-Borel. Como consequencia, provamos resultados de existência e aproximação de soluções de equações de convulção nos espaços de funções (s; (r , q))-quase-nucleares de um dado tipo e uma dada ordem / Abstract: In this work we introduce the spaces of (s; m (r , q))-summing functions of a given type and order defined in E, and the spaces of (s; (r, q))-quasi-nuclear functions of a given type and order defined in E, and we prove that the Fourier-Borel transform identify the dual of the space of (s; (r; q))-quasi-nuclear functions of a given type and order defined in E, with the space of (s' ; m (r'; q'))-summing functions of a corresponding type and order defined in E'. We also prove division theorems for (s; m (r; q))-summing functions of a given type and order and division theorems involving the Fourier-Borel transform. As a consequence we prove the existence and approximation results for convolution equations on the spaces of (s; (r; q))-quasi-nuclear functions of a given type and order / Doutorado / Analise Funcional / Doutor em Matemática

Orientador: Jorge Tulio Mujica Ascui / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-07T16:44:31Z (GMT). No. of bitstreams: 1 Takatsuka_Paula_D.pdf: 3540981 bytes, checksum: 643e40ac81900cf042cfe1cfb3737b0d (MD5) Previous issue date: 2006 / Resumo: Este trabalho estende teoremas clássicos da teoria de funções holomorfas de uma variável complexa para espaços localmente convexos de dimensão infinita. Serão dadas várias caracterizações de famílias normais, n¿ao apenas com relação à topologia compacto-aberta, mas também para outras topologias naturais no espaço de aplicações holomorfas. Teoremas de tipo Montel e de tipo Schottky, bem como outros resultados correlatos, ser¿ao estabelecidos em dimensão infinita para as diferentes topologias. Teoremas de limita¸c¿ao universal sobre famílias de funções holomorfas que omitem dois valores distintos ser¿ao formulados para espaços de Banach / Abstract: The present work extends some classical theorems from the theory of holomorphic functions of one complex variable to infinite dimensional locally convex spaces. Several characterizations of normal families are given, not only for the compact-open topology, but also for other natural topologies on spaces of holomorphic mappings. Montel-type and Schottky-type theorems and various related results are established in infinite dimension for these different topologies. Universal boundedness theorems concerning families of holomorphic functions which omit two distinct values are formulated for Banach spaces / Doutorado / Mestre em Matemática