by Yun-ming Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 92-93). / Chapter Chapter 1 --- Sequence Spaces / Chapter 1.1 --- Sequence spaces --- p.1 / Chapter 1.2 --- "Duality theorems on <λ, λX>" --- p.6 / Chapter 1.3 --- Topological properties of sequence spaces --- p.30 / Chapter 1.4 --- Diagonal maps --- p.41 / Chapter Chapter 2 --- Vector sequence spaces / Chapter 2.1 --- λ-summability of vector sequences --- p.48 / Chapter 2.2 --- "A duality theorem on <Λ(E),Λ(E)X>" --- p.62 / Chapter 2.3 --- "The topological duals of [λ[E],II(ρ,ξ)},(λ(E)(ρ,ξ)) and [ λw(E), B(ρ,ξ) ]" --- p.75 / Chapter 2.4 --- Fundamentally λ-bounded spaces --- p.86 / Reference --- p.92

Thesis (Ph. D.)--Lehigh University, 1999. / Includes vita. Bibliography: leavf 21.

Thesis (doctoral)--University of Tartu, 2006. / This dissertation is based on 5 papers. Includes bibliographical references

The class of sequential spaces and its successive smaller subclasses, the Fréchet spaces and the first-countable spaces, have topologies which are completely specified by their convergent sequences. Because sequences have many advantages over nets, these topological spaces are of interest. Special attention is paid to those properties of first-countable spaces which can or cannot be generalized to Fréchet or sequential spaces. For example, countable compactness and sequential compactness are equivalent in the larger class of sequential spaces. On the other hand, a Fréchet space with unique sequential limits need not be Hausdorff, and there is a product of two Fréchet spaces which is not sequential. Some of the more difficult problems are connected with products. The topological product of an arbitrary sequential space and a T₃ (regular and T₁) sequential space X is sequential if and only if X is locally countably compact. There are also several results which demonstrate the non-productive nature of Fréchet spaces. The sequential spaces and the Fréchet spaces are precisely the quotients and continuous pseudo-open images, respectively, of either (ordered) metric spaces or (ordered) first-countable spaces. These characterizations follow from those of the generalized sequential spaces and the generalized Fréchet spaces. The notions of convergence subbasis and convergence basis play an important role here. Quotient spaces are characterized in terms of convergence subbases, and continuous pseudo-open images in terms of convergence bases. The equivalence of hereditarily quotient maps The class of sequential spaces and its successive smaller subclasses, the Fréchet spaces and the first-countable spaces, have topologies which are completely specified by their convergent sequences. Because sequences have many advantages over nets, these topological spaces are of interest. Special attention is paid to those properties of first-countable spaces which can or cannot be generalized to Fréchet or sequential spaces. For example, countable compactness and sequential compactness are equivalent in the larger class of sequential spaces. On the other hand, a Fréchet space with unique sequential limits need not be Hausdorff, and there is a product of two Fréchet spaces which is not sequential. Some of the more difficult problems are connected with products. The topological product of an arbitrary sequential space and a T₃ (regular and T₁) sequential space X is sequential if and only if X is locally countably compact. There are also several results which demonstrate the non-productive nature of Fréchet spaces. The sequential spaces and the Fréchet spaces are precisely the quotients and continuous pseudo-open images, respectively, of either (ordered) metric spaces or (ordered) first-countable spaces. These characterizations follow from those of the generalized sequential spaces and the generalized Fréchet spaces. The notions of convergence subbasis and convergence basis play an important role here. Quotient spaces are characterized in terms of conver-gence subbases, and continuous pseudo-open images in terms of convergence bases. The equivalence of hereditarily quotient maps and continuous pseudo-open maps implies the latter result. and continuous pseudo-open maps implies the latter result. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.

In this paper the weak completeness of certain sequence spaces is examined. In particular, we show that each of the sequence spaces c0 and 9, 1 < p < c, is a Banach space. A Riesz representation for the dual space of each of these sequence spaces is given. A Riesz representation theorem for Hilbert space is also proven. In the third chapter we conclude that any reflexive space is weakly (sequentially) complete. We give 01 as an example of a non-reflexive space that is weakly complete. Two examples, c0 and YJ, are given of spaces that fail to be weakly complete.

In this thesis, we study weighted composition operatorsT(xn)=(£fnX£m(n)) between sequence spaces(c0,c,l1,lp), and more precisely, the sufficient and necessary condition that they are compact. First,we obtain some results of weighted composition operators beingcompact, weakly compact and completely continuous on c0 spaces. Then, we extend then to c,l1,and lp(1<p<¡Û) spaces. Finally, we obtain the condition that an operator from c0, c or lp into c0, c, or lq is compact, weakly compact or completely continuous.

Made available in DSpace on 2015-05-15T11:46:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 337158 bytes, checksum: afe6aba5da9618c6fdc4d945e9b294e4 (MD5) Previous issue date: 2012-07-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The notion of lineability emerged in the eighties, albeit its essence is quite older, as a method to measure the existence of linear structures in a priori nonlinear frameworks. More precisely, a subset of a topological vector space is lineable (spaceable) if it contains, except eventually for the null vector, an infinite-dimentional subspace (infinite- dimensional closed subspace). In this work we investigate lineability and spaceability in the context of norm attaining operators and sequence spaces. / A noção de lineabilidade surgiu nos anos 80, embora a essência da ideia seja bem anterior, como uma forma de medir a existência de estruturas lineares em ambientes a priori não lineares. Mais precisamente, um subconjunto de um espaço vetorial topológico é lineável (espaçável) se ele contiver, exceto possivelmente pelo vetor nulo, um subespaço (subespaço fechado) de dimensão infinita. Neste trabalho estudamos resultados de lineabilidade e espaçabilidade no contexto de operadores lineares que atingem a norma e também em espaços de sequências.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T19:03:09Z No. of bitstreams: 1 Arquivototal.pdf: 737510 bytes, checksum: a205d9714f9ec661929aea54c8a55145 (MD5) / Made available in DSpace on 2018-05-02T19:03:09Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 737510 bytes, checksum: a205d9714f9ec661929aea54c8a55145 (MD5) Previous issue date: 2017-08-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The main goal of this work is to study a new sequence space introduced in 2014 by Karn and Sinha, namely the space of mid p-summable sequences. More speci cally, we will study a recent work by G. Botelho and J.R. Campos, which deepens the seminal study of this space and presents new classes of operators involving the new space and the classical sequence spaces of absolutely and weakly p-summable sequences, called absolutely mid p-summing and weakly mid p-summing operators. From this, we study a new factorization theorem, involving these new classes of operators, for the absolutely p-summing operators. / O principal objetivo desta dissertação é estudar um novo espaço de sequências introduzido por Karn e Sinha em 2014, a saber, o espaçoo das sequências mid p-somáveis. Mais especi camente, estudaremos um recente trabalho de G. Botelho e J. R. Campos que aprofunda o estudo seminal do espa co e apresenta novas classes de operadores envolvendo este novo espa co e os espa cos cl assicos de sequ^encias absolutamente e fracamente p-somáveis, denominados operadores absolutamente mid p-somantes e operadores fracamente mid p-somantes. A partir disto, estudamos um novo teorema de fatoração, envolvendo estas novas classes de operadores, para os operadores absolutamente p-somantes. mid p-somáveis; Operadores absolutamente e fracamente mid p-somantes.

Cette thèse contient des contributions originales à la théorie du Contrôle Optimal en temps discret et en horizon infini du point de vue de Pontryagin. Il y a 5 chapitres dans cette thèse. Dans le chapitre 1, nous rappelons des résultats préliminaires sur les espaces de suites à valeur dans et des résultats de Calcul Différentiel. Dans le chapitre 2, nous étudions le problème de Contrôle Optimal, en temps discret et en horizon infini avec la contrainte asymptotique et avec le système autonome. En utilisant la structure d'espace affine de Banach de l'ensemble des suites convergentes vers 0, et la structure d'espace vectoriel de Banach de l'ensemble des suites bornées, nous traduisons ce problème en un problème d'optimisation statique dam des espaces de Banach. Après avoir établi des résultats originaux sur les opérateurs de Nemytskii sur les espaces de suites et après avoir adapté à notre problème un théorème d'existence de multiplicateurs, nous établissons un nouveau principe de Pontryagin faible pour notre problème. Dans le chapitre 3, nous établissons un principe de Pontryagin fort pour les problèmes considérés au chapitre 2 en utilisant un résultat de Ioffe-Tihomirov. Le chapitre 4 est consacré aux problèmes de Contrôle Optimal, en temps discret et en horizon infini, généraux avec plusieurs critères différents. La méthode utilisée est celle de la réduction à l'horizon fini, initiée par J. Blot et H. Chebbi en 2000. Les problèmes considérés sont gouvernés par des équations aux différences ou des inéquations aux différences. Un nouveau principe de Pontryagin faible est établi en utilisant un résultat récent de J. Blot sur les multiplicateurs à la Fritz John. Le chapitre 5 est consacré aux problèmes multicritères de Contrôle Optimal en temps discret et en horizon infini. De nouveaux principes de Pontryagin faibles et forts sont établis, là-aussi en utilisant des résultats récents d'optimisation, sous des hypothèses plus faibles que celles des résultats existants. / This thesis contains original contributions to the optimal control theory in the discrete-time framework and in infinite horizon following the viewpoint of Pontryagin. There are 5 chapters in this thesis. In Chapter 1, we recall preliminary results on sequence spaces and on differential calculus in normed linear space. In Chapter 2, we study a single-objective optimal control problem in discrete-time framework and in infinite horizon with an asymptotic constraint and with autonomous system. We use an approach of functional analytic for this problem after translating it into the form of an optimization problem in Banach (sequence) spaces. Then a weak Pontyagin principle is established for this problem by using a classical multiplier rule in Banach spaces. In Chapter 3, we establish a strong Pontryagin principle for the problems considered in Chapter 2 using a result of Ioffe and Tihomirov. Chapter 4 is devoted to the problems of Optimal Control, in discrete time framework and in infinite horizon, which are more general with several different criteria. The used method is the reduction to finite-horizon initiated by J. Blot and H. Chebbi in 2000. The considered problems are governed by difference equations or difference inequations. A new weak Pontryagin principle is established using a recent result of J. Blot on the Fritz John multipliers. Chapter 5 deals with the multicriteria optimal control problems in discrete time framework and infinite horizon. New weak and strong Pontryagin principles are established, again using recent optimization results, under lighter assumptions than existing ones.