Inverse problems in (exploration) seismology are known for their large to very large scale. For instance, certain sparsity-promoting inversion techniques involve vectors that easily exceed 230 unknowns while seismic imaging involves the construction and application of matrix-free discretized operators where single matrix-vector evaluations may require hours, days or even weeks on large compute clusters. For these reasons, software development in this field has remained the domain of highly technical codes programmed in low-level languages with little eye for easy development, code reuse and integration with (nonlinear) programs that solve inverse problems. Following ideas from the Symes’ Rice Vector Library and Bartlett’s C++ object-oriented interface, Thyra, and Reduction/Transformation operators (both part of the Trilinos software package), we developed a software-development environment based on overloading. This environment provides a pathway from in-core prototype development to out-of-core and MPI ’production’ code with a high level of code reuse. This code reuse is accomplished by integrating the out-of-core and MPI functionality into the dynamic object-oriented programming language Python. This integration is implemented through operator overloading and allows for the development of a coordinate-free solver framework that (i) promotes code reuse; (ii) analyses the statements in an abstract syntax tree and (iii) generates executable statements. In the current implementation, we developed an interface to generate executable statements for the out-of-core unix-pipe based (seismic) processing package RSF-Madagascar (rsf.sf.net). The modular design allows for interfaces to other seismic processing packages and to in-core Python packages such as numpy. So far, the implementation overloads linear operators and elementwise reduction/transformation operators. We are planning extensions towards nonlinear operators and integration with existing (parallel) solver frameworks such as Trilinos.

For 0 < |q| < 1, the q-numerical range is defined on the algebra Mn of all n x n complex matrices by Wq(A) ={x*Ay : x, y Є Cn , x*x = y*y = 1, x* y = q}. The q-numerical radius is defined by rq(A) = max{|μ| : μ Є Wq(A)}. We characterize isometries of the metric space (Mn , rq) i.e., the maps φ : Mn → Mn that satisfy rq(A - B) = rq(φ(A) - φ(B)). We also characterise maps on Mn that preserve the q-numerical range.

Thesis (M.Sc.)--Memorial University of Newfoundland, 1995. / Typescript. Computer disk contains: Appendix A, Fortran programs. Bibliography: leaves 134-137. Also available online.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (p. [77]-79).

Thesis (doctoral)--Technische Hogeschool Eindhoven, 1983. / Text in English ; summary and vita in Dutch. Includes indexes. Vita. Includes bibliographical references (p. 190-193).

Orientador: Jorge Tulio Mujica Ascui / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação / Made available in DSpace on 2018-08-04T19:54:16Z (GMT). No. of bitstreams: 1 Jatoba_AriosvaldoMarques_M.pdf: 1695585 bytes, checksum: 3e9af91b8444dc2cdb0bfefa05a23872 (MD5) Previous issue date: 2005 / Resumo: Nosso primeiro objetivo é provar uma importante caracterização de conjuntos fracamente compactos em espaços de Banach, o Teorema de Eberlein-Smulian, que diz que um subconjunto K de um espaço de Banach é fracamente compacto se, e somente se, toda seqüência em K tem uma subseqüência que converge fracamente para um elemento de K. Em seguida nós provamos uma importante caracterização de operadores fracamente compactos entre espaços de Banach, o Teorema de Gantmacher, que diz que um operador linear contínuo T: E -> F entre espaços de Banach é fracamente compacto se, e somente se, o seu adjunto T': F'-> E' é fracamente compacto. Finalmente, nós provamos o resultado principal deste trabalho, o Teorema de Fatoração de Davis, Figiel, Johnson e Pelczynski, que diz que, um operador linear contínuo T: E -> F entre espaços deBanach é fracamente compacto se, e somente se, T fatora-se através de um espaço de Banach reflexivo, isto é, existem um espaço de Banach reflexivo G e operadores lineares contínuos S: E-> G and L: G -> F tais que T = L o S. U ma aplicação deste resultado é que um polinômio m- homogêneo contínuo P: E -> F entre espaços de Banach é fracamente compacto se, e somente se, existem um espaço de Banach reflexivo G, um polinômio contínuo m-homogêneo Q: E-> G e um operador linear contínuo L: G -> F tais que P = L o Q / Abstract: Our first aim is to prove an important caracterization of weakly compact sets in Banach spaces, the Eberlein-¿mulian Theorem which says that a subset K of a Banach space is weakly compact if and only if each sequence in K has a subsequence which converges weakly to an element of K. We next prove an important caracterization of weakly compact operators between Banach spaces, the Gantmacher Theorem, which says that a continuous linear operator T: E -> F between Banach spaces is weakly compact if and only if its adjoint T': F'-> E' is weakly compact. Finally, we prove the principal result of this work, the Factorization Theorem of Davis, Figiel, Johnson and Pelczynski, which says that a continuous linear operator T: E -> F between Banach spaces is weakly compact if and only if T factors through a reflexive Banach space, i.e, there are a reflexive Banach space G and continuous linear operators S: E-> G and L: G -> F such that T = L o S. An application of this result is that an m-homogeneous continuous polynomial P: E -> F between Banach spaces is weakly compact if and only if there are a reflexive Banach space G, an m-homogeneous continuous polynomial Q: E -> G and a continuous linear operator L: G -> F such that P = L o Q / Mestrado / Analise Funcional / Mestre em Matemática

Orientador: Mario Carvalho de Matos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T22:15:35Z (GMT). No. of bitstreams: 1 CernaMaguina_BibianoMartin_D.pdf: 1394612 bytes, checksum: ca6a283533782089f15a071899a0ffd2 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho, damos uma generalização do conceito e da teoria das aplicações lineares p-fatoráveis para o caso multilinear. Fornecemos duas definições; baseadas na definição 2.2 chegamos a obter alguns resultados. Seguindo a ideas do Pietsch, e baseada na definição 3.9 previa generalização de algumas definições e teoremas dos ideais lineares para o caso multilinear tentamos provar a equivalência das duas definições / Abstract: In this work, we give one generalization of the concept and the linear theory of applications p - factories for the multilinear case. We supply two definitions; based in definition 2.2 we arrive to get some results. Following the ideas of the Pietsch, and based in definition 3.9 it foresaw generalization of some definitions and theorems of the linear ideals for the multilinear case we try to prove the equivalence of the two definitions / Doutorado / Matematica / Doutor em Matemática

Orientador: Jorge Tulio Mujica Ascui / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T09:42:47Z (GMT). No. of bitstreams: 1 Miyamura_MauricioYudi_M.pdf: 634948 bytes, checksum: 09f557fd6fcd4987f744c3d9c645f602 (MD5) Previous issue date: 2007 / Resumo: Sejam E e F espaços de Banach. Os principais resultados que iremos expor serão teoremas sobre a reflexividade de L (E; F) e P (mE; F).. No capítulo 2, estudamos alguns conceitos básicos da teoria de produtos tensoriais de espaços de Banach. A importância do capítulo 2 para o trabalho seria, essencialmente, a identificação do espaço de operadores lineares contínuos L (E; F) com o dual do produto tensorial projetivo E ÄpF?. No capítulo 3, que trata de espaços de polinômios homogêneos, incluímos de noções e resultados básicos e estudamos um teorema de linearização que permitirá transferir resultados em espaços de operadores lineares para espaços de polinômios homogêneos. / Abstract: Let E and F be Banach spaces. The main results in this work are theorems concerning the reflexivity of L (E; F) and P (mE; F). In Chapter 2, we study basic concepts of the theory of tensor products of Banach spaces. The importance of Chapter 2 will be, essentially, the identification of the space of continuous linear operators L(E; F) with the dual of the projective tensor product E ÄpF?. In Chapter 3, that deals with homogeneous polynomials, we include basic definitions and results and we study a linearization theorem that will allow to transfer results from spaces of linear operators to spaces of homogeneous polynomials. / Mestrado / Matematica / Mestre em Matemática

If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property.

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = Xr1 + Xr2 + ... + Xrt and r1>r2>...>rt≥2. In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We also extended these results to linear operators that strongly preserve the matrix polynomial equation p(X) = I where p(X) is as above. Chapters I and II of this thesis contain background material and summaries of the work done by other researchers on the linear preserver problem. Characterizations of linear operators in chapters III, IV, V, and VI of this thesis are new.