Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

A BROADER CONTEXT FOR MONOTONICALLY MONOLITHIC SPACES

This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically kappa-monolithic space for any infinite cardinal kappa and present the relevant results. We show, among other things, that any sigma-product of monotonically kappa-monolithic spaces is monotonically kappa-monolithic for any infinite cardinal kappa; besides, it is consistent that any strongly monotonically omega-monolithic space with caliber omega(1) is second countable. We also study (strong) monotone kappa-monolithicity in linearly ordered spaces and subspaces of ordinals.

The Role of Gay Spaces for a Gay Destination : Gay Tourism in Gran Canaria

This thesis has the aim to evaluate the role of gay spaces in Gran Canaria as a gay tourists destination with particular reference to gay exclusive resorts. The validation of the gay identity is a key motivation for homosexuals to travel, in order to connect with other homosexuals and experience the gay life that they might not be able to experience at home. Gay spaces have been defined both as liberated areas as well as ghettos, where the homosexuals are, in a way, restrained. The method chosen, a small number of semi- structured interviews with managers of gay exclusive resorts in Maspalomas, the hub of gay life in Gran Canaria, where major LGBT events are held, there is a gay friendly environment, a thriving gay scene and many gay exclusive resorts. In the case of Gran Canaria the gay-specific offer is complementary to the ‘regular’ tourism offer, as they coexist, complement and at times overlap. Nevertheless the gay centric holiday is still predominant amongst gay men, and it is likely to continue to be according to the informants. This is because gay tourists seek freedom and a sense of inclusion that they would not be able to find in mixed environments.

Just which Reality do you Mean? Users' Experiences of Virtual Spaces

Virtual Reality is a relatively new technology in the relatively young field of computer science. The design of Virtual Reality has only recently come into discussion, as well as the implications for this sort of design. I hope to determine how a user can work most efficiently and accurately in a Virtual World. By studying this, I hope to help in the standardization of Virtual Reality design.

Radon surveys in Brazil using CR-39

In this work results of two radon daughters survey in Brazil are presented and discussed. Some methodological problems concerning the first survey are pointed out which were corrected for the second survey in order to make a realistic long-term measurement of radon decay products in the air. The technique employed in both surveys was the alpha-spectroscopy using CR-39. The reliability of this technique as well as the results of the second survey are discussed, which indicate a poor correlation between radon and its decay products in the air at the researched dwellings. (c) 2005 Elsevier Ltd. All rights reserved.

Effects of environrnental conditions on the radon daughters spatial distribution

The influence of environmental conditions on the indoor radon daughters spatial distribution is studied both theoretically and experimentally. Simple theoretical calculations indicate that ventilation and variation in the size distribution of aerosols should play an important role influencing the spatial distribution of indoor radon decay products, but experimental results indicate that these environmental factors have little influence on the spatial distribution of radon daughters near the walls of indoor environments. We have observed that the maximum effective range of the plate-out effect varies only between I and 3 cm in typical dwellings. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Parâmetro de regularização em problemas inversos: estudo numérico com a transformada de Radon

In general, an inverse problem corresponds to find a value of an element x in a suitable vector space, given a vector y measuring it, in some sense. When we discretize the problem, it usually boils down to solve an equation system f(x) = y, where f : U Rm ! Rn represents the step function in any domain U of the appropriate Rm. As a general rule, we arrive to an ill-posed problem. The resolution of inverse problems has been widely researched along the last decades, because many problems in science and industry consist in determining unknowns that we try to know, by observing its effects under certain indirect measures. Our general subject of this dissertation is the choice of Tykhonov´s regulaziration parameter of a poorly conditioned linear problem, as we are going to discuss on chapter 1 of this dissertation, focusing on the three most popular methods in nowadays literature of the area. Our more specific focus in this dissertation consists in the simulations reported on chapter 2, aiming to compare the performance of the three methods in the recuperation of images measured with the Radon transform, perturbed by the addition of gaussian i.i.d. noise. We choosed a difference operator as regularizer of the problem. The contribution we try to make, in this dissertation, mainly consists on the discussion of numerical simulations we execute, as is exposed in Chapter 2. We understand that the meaning of this dissertation lays much more on the questions which it raises than on saying something definitive about the subject. Partly, for beeing based on numerical experiments with no new mathematical results associated to it, partly for being about numerical experiments made with a single operator. On the other hand, we got some observations which seemed to us interesting on the simulations performed, considered the literature of the area. In special, we highlight observations we resume, at the conclusion of this work, about the different vocations of methods like GCV and L-curve and, also, about the optimal parameters tendency observed in the L-curve method of grouping themselves in a small gap, strongly correlated with the behavior of the generalized singular value decomposition curve of the involved operators, under reasonably broad regularity conditions in the images to be recovered

Quasiprobability distribution functions for periodic phase spaces: I. Theoretical aspects

An approach featuring s-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle - angular momentum coherent states must be constructed in an appropriate fashion.