Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.

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.

Filmljudets funktioner i krigsfilm : En audio-visuell analys av Apocalypse Now och Saving Private Ryan

I denna uppsats har filmljudet i krigsfilmerna Apocalypse Now och Saving Private Ryan undersökts. Detta har gjorts för att försöka bidra med ökad förståelse för filmljudets användningsområde och funktioner, främst för filmerna i fråga, men även för krigsfilm rent generellt. Filmljud i denna kontext omfattar allt det ljud som finns i film, men utesluter dock all ickediegetisk musik. Båda filmerna har undersökts genom en audio-visuell analys. En sådan analys görs genom att detaljgranska båda filmernas ljud- och bildinnehåll var för sig, för att slutligen undersöka samma filmsekvens som helhet då ljudet och bilden satts ihop igen. Den audio-visuella analysmetod som nyttjats i uppsatsen är Michel Chions metod, Masking. De 30 minuter film som analyserades placerades sedan i olika filmljudzoner, där respektive filmljudzons ljudinnehåll bland annat visade vilka främsta huvudfunktioner somfilmljudet hade i dessa filmer. Dessa funktioner är till för att bibehålla åskådarens fokus och intresse, att skapa närhet till rollkaraktärerna, samt att tillföra en hög känsla av realism och närvaro. Intentionerna med filmljudet verkade vara att flytta åskådaren in i filmens verklighet, att låta åskådaren bli ett med filmen. Att återspegla denna känsla av realism, närvaro, fokus samt intresse, visade sig också vara de intentioner som funnits redan i de båda filmernas förproduktionsstadier. Detta bevisar att de lyckats åstadkomma det de eftersträvat. Men om filmljudet använts på samma sätt eller innehar samma funktioner i krigsfilm rent genrellt går inte att säga.I have for this bachelor’s thesis examined the movie sound of the classic warfare movies Apocalypse Now and Saving Private Ryan. This is an attempt to contribute to a more profound comprehension of the appliance and importance of movie sound. In this context movie sound implies all kinds of sounds within the movies, accept from non-diegetic music. These two movies have been examined by an audio-visual analysis. It's done by auditing the sound and picture content separately, and then combined to audit the same sequence as a whole. Michel Chion, which is the founder of this analysis, calls this method Masking. The sound in this 30 minute sequence was then divided into different zones, where every zone represented a certain main function. These functions are provided to create a stronger connection to the characters, sustain the viewers interest and bring a sense of realism and presence. It seems though the intention with the movies sound is to bring the viewers to the scene in hand, and let it become their reality. To mirror this sense of realism, presence, focus and interest, proves to be the intention from an early stage of the production. This bachelor’s thesis demonstrates a success in their endeavours. Although it can’t confirm whether the movie sound have been utilized in the same manner or if they posess the same functions to warefare movies in general.

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.

Globalization, Agency, and Institutional Innovation: The Rise of Public-Private Partnerships in Global Governance

Public and private actors increasingly cooperate in global governance, a realm previously reserved for states and intergovernmental organizations (IOs). This trend raises fascinating theoretical questions. What explains the rise in public-private institutions and their role in international politics? Who leads such institutional innovation and why? To address the questions, this paper develops a theory of the political demand and supply of public-private institutions and specifies the conditions under which IOs and non-state actors would cooperate, and states would support this public-private cooperation. The observable implications of the theoretical argument are evaluated against the broad trends in public-private cooperation and in a statistical analysis of the significance of demand and supply-side incentives in public-private cooperation for sustainable development. The study shows that public-private institutions do not simply fill governance gaps opened by globalization, but cluster in narrower areas of cooperation, where the strategic interests of IOs, states, and transnational actors intersect.

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.