The Range of a Module Measure Defined on an Effect Algebra

Effect algebras are the main object of study in quantum mechanics. Module measures are those measures defined on an effect algebra with values on a topological module. Let R be a topological ring and M a topological R-module. Let L be an effect algebra. The range of a module measure mu : L -> M is studied. Among other results, we prove that if L is an sRDP sigma-effect algebra with a natural basis and mu : L -> R is a countably additive measure, then mu has bounded variation

Chaos in Topological Modules

Chaotic and pathological phenomena in topological modules are studied in this manuscript. In particular, constructions of noncontinuous linear functionals are provided for a wide variety of topological modules. In addition, constructions of balanced and absorbing sets which are not neighborhoods of zero are also given in an extensive class of topological modules. Finally, we construct a linearly open set with empty interior in a large amount of topological modules. All these constructions are related to each other. Prior to developing all these results, we provide an axiomatization of the topological concept of limit by introducing the limit operators in a similar context as hull operators or closure operators are defined

Regularity in Topological Modules

The framework of Functional Analysis is the theory of topological vector spaces over the real or complex field. The natural generalization of these objects are the topological modules over topological rings. Weakening the classical Functional Analysis results towards the scope of topological modules is a relatively new trend that has enriched the literature of Functional Analysis with deeper classical results as well as with pathological phenomena. Following this trend, it has been recently proved that every real or complex Hausdorff locally convex topological vector space with dimension greater than or equal to 2 has a balanced and absorbing subset with empty interior. Here we propose an extension of this result to topological modules over topological rings. A sufficient condition is provided to accomplish this extension. This sufficient condition is a new property in topological module theory calledstrong open property. On the other hand, topological regularity of closed balls and open balls in real or complex normed spaces is a trivial fact. Sufficient conditions, related to the strong open property, are provided on seminormed modules over an absolutely semivalued ring for closed balls to be regular closed and open balls to be regular open. These sufficient conditions are in fact characterizations when the seminormed module is the absolutely semivalued ring. These characterizations allow the provision of more examples of closed-unit neighborhoods of zero. Consequently, the closed-unit ball of any unital real Banach algebra is proved to be a closed-unit zero-neighborhood. We finally transport all these results to topological modules over topological rings to obtain nontrivial regular closed and regular open neighborhoods of zero. In particular, ifMis a topologicalR-module and m* is an element of M* is a continuous linear functional on M which is open as a map between topological spaces, then m*-1(int(B)) is regular open and m*-1(B) is regular closed, for B any closed-unit zero-neighborhood in R

Pre-Schauder Bases in Topological Vector Spaces

A Schauder basis in a real or complex Banach space X is a sequence (en)n is an element of N in X such that for every x is an element of X there exists a unique sequence of scalars (lambda n)n is an element of N satisfying that x= n-ary sumation n=1 infinity lambda nen. Schauder bases were first introduced in the setting of real or complex Banach spaces but they have been transported to the scope of real or complex Hausdorff locally convex topological vector spaces. In this manuscript, we extend them to the setting of topological vector spaces over an absolutely valued division ring by redefining them as pre-Schauder bases. We first prove that, if a topological vector space admits a pre-Schauder basis, then the linear span of the basis is Hausdorff and the series linear span of the basis minus the linear span contains the intersection of all neighborhoods of 0. As a consequence, we conclude that the coefficient functionals are continuous if and only if the canonical projections are also continuous (this is a trivial fact in normed spaces but not in topological vector spaces). We also prove that, if a Hausdorff topological vector space admits a pre-Schauder basis and is w*-strongly torsionless, then the biorthogonal system formed by the basis and its coefficient functionals is total. Finally, we focus on Schauder bases on Banach spaces proving that every Banach space with a normalized Schauder basis admits an equivalent norm closer to the original norm than the typical bimonotone renorming and that still makes the basis binormalized and monotone. We also construct an increasing family of left-comparable norms making the normalized Schauder basis binormalized and show that the limit of this family is a right-comparable norm that also makes the normalized Schauder basis binormalized

f -Statistical convergence on topological modules

The classical notion of statistical convergence has recently been transported to the scope of real normed spaces by means of the f -statistical convergence for f a modulus function. Here, we go several steps further and extend the f -statistical convergence to the scope of uniform spaces, obtaining particular cases of f -statistical convergence on pseudometric spaces and topological modules.The first author has been partially supported by Research Grant PGC-101514-B-I00 awarded by the Ministry of Science, Innovation and Universities of Spain. This work has also been co-financed by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia, under Project Reference FEDER-UCA18-105867

On f-strongly Cesàro and f-statistical derivable functions

In this manuscript, we introduce the following novel concepts for real functions related to f-convergence and f-statistical convergence: f-statistical continuity, f-statistical derivative, and f-strongly Cesaro derivative. In the first subsection of original results, the f-statistical continuity is related to continuity. In the second subsection, the f-statistical derivative is related to the derivative. In the third and final subsection of results, the f-strongly Cesaro derivative is related to the strongly Cesaro derivative and to the f-statistical derivative. Under suitable conditions of the modulus f, several characterizations involving the previous concepts have been obtained.The second author has been partially supported by Research Grant PGC-101514-B-I00 awarded by the Ministry of Science, Innovation and Universities of Spain. This work has also been co-financed by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia, under Project Reference FEDERUCA18-105867. The APC has been paid by the Department of Mathematics of the University of Cadiz

Funciones narrativas del personaje femenino en el cómic y la animación japonesa para adolescentes masculinos

El cómic japonés (manga) y la animación japonesa (anime) son poderosas industrias culturales que, progresivamente, se han ido expandiendo internacionalmente. A medida que estas obras han ido llegando a los mercados occidentales, la atención de los investigadores se ha fijado en las particularidades expresivas, narrativas y culturales de estos productos. La investigación en género relacionada con el manga y el anime se ha centrado principalmente en las obras destinadas a un público femenino y, salvo escasas investigaciones, se ha tendido a obviar el estudio de los productos orientados al público masculino. La presente comunicación recoge los resultados del análisis de los personajes femeninos que aparecen en el shounen manga y anime, un género orientado hacia adolescentes masculinos cuya temática se centra en historias de acción y aventuras. La metodología de análisis se basa en el estudio de los personajes como roles según la narrativa audiovisual, de modo que ha sido posible identificar los tipos de personajes más habituales en estos relatos a partir de las funciones que desempeñan. Los datos aparecen recogidos en un catálogo que analiza las características narrativas del personaje femenino y presta especial atención a las funciones más habituales: las de sujeto amoroso, aliada, objeto amoroso, víctima y enemiga

Arquetipos iconográficos femeninos en el cómic y la animación japonesa para adolescentes masculinos

El cómic japonés (manga) y la animación japonesa (anime) son poderosas industrias culturales que, progresivamente, se han ido expandiendo internacionalmente. A medida que estas obras han ido llegando a los mercados occidentales, la atención de los investigadores se ha fijado en las particularidades expresivas, narrativas y culturales de estos productos. La investigación en género relacionada con el manga y el anime se ha centrado principalmente en las obras destinadas a un público femenino y, salvo escasas investigaciones, se ha tendido a obviar el estudio de los productos orientados al público masculino. La presente ponencia recoge los resultados del análisis de los personajes femeninos presentes en el shounen manga y anime, un género orientado hacia adolescentes masculinos cuya temática se centra en historias de acción y aventuras. Tras observar detenidamente la construcción de estos personajes femeninos, se realiza una catalogación de los principales arquetipos iconográficos presentes en dicho género y se recogen las principales características de los personajes femeninos en función de su edad, su apariencia, atractivo físico, su vestuario y otros rasgos característicos

General methods of convergence and summability

This paper is on general methods of convergence and summability. We first present the general method of convergence described by free filters of N and study the space of convergence associated with the filter. We notice that c(X) is always a space of convergence associated with a filter (the Frechet filter); that if X is finite dimensional, then l infinity (X) is a space of convergence associated with any free ultrafilter of N; and that if X is not complete, then l infinity (X) is never the space of convergence associated with any free filter of N. Afterwards, we define a new general method of convergence inspired by the Banach limit convergence, that is, described through operators of norm 1 which are an extension of the limit operator. We prove that l infinity (X) is always a space of convergence through a certain class of such operators; that if X is reflexive and 1-injective, then c(X) is a space of convergence through a certain class of such operators; and that if X is not complete, then c(X) is never the space of convergence through any class of such operators. In the meantime, we study the geometric structure of the set HB(lim):={T is an element of B(l infinity (X),X):T|c(X)=lim and parallel to T parallel to =1} and prove that HB(lim) is a face of BLX0 if X has the Bade property, where LX0:={T is an element of B(l infinity (X),X):c0(X)subset of ker(T)}. Finally, we study the multipliers associated with series for the above methods of convergence

Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence

[EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We also obtain generalizations of some results regarding uniform convergence of unconditionally convergent series through the concept of statistical convergence. Finally, we provide a version of the Orlicz- Pettis theorem for A-multiplier convergent operator series by means of the statistical convergence.The first author has been supported by Research Grant PGC-101514-B-I00 awarded by the Ministry of Science, Innovation and Universities of Spain, and by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia, with project reference: FEDER-UCA18-105867. The third author has been supported by MCIN/AEI/10.13039/501100011033, Project PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEU/2021/070.García-Pacheco, FJ.; Kama, R.; Murillo Arcila, M. (2022). Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence. Results in Mathematics. 77(1):1-16. https://doi.org/10.1007/s00025-021-01582-411677