Abstract. Consider an operator T : X(µ) → Y (µ) between Banach function spaces having adequate order continuity and Fatou properties. Assume that T can be factorized through a Banach space as T = R • S, where R and the adjoint of S are p-th power and q-th power factorable, respectively. Then a canonical factorization scheme can be given for T . We show that it provides a tool for analyzing T that becomes specially useful for the case of kernel operators. In particular, we show that this square factorization scheme for T is equivalent to some inequalities for the bilinear form defined by T . Kernel operators are studied from this point of view.Primary 46E30, Secondary 47B38, 46B42, 46B28 Banach function spaces, Köthe duality, p-th power factorable operators, factorization, kernel operators.
Las curvas de Bézier, un instrumento matemático para la modelización de curvas y superficies, nacieron como una aplicación concreta en el seno de la industria automovilística. El presente artículo pretende recuperar este ejemplo para mostrar como ciertos desarrollos matemáticos que surgieron directamente en la industria, pueden utilizarse como contenidos en la enseñanza universitaria. Explicaremos cómo y por qué surgen, y también su formulación matemática junto con alguno de los problemas que plantea. Para finalizar describimos una experiencia en el aula y extraemos algunas conclusiones respecto a una hipotética incorporación de una asignatura enfocada a la resolución de un determinado diseño utilizando curvas y superficies de Bézier.The Bézier curves, a mathematical tool used in construction of curves and surfaces, was born as concrete application within the car industry. The present paper expects to recover this example for show how some mathematical tools can be used in the university teaching. We explain how and why these arise and also its mathematical formulation with the troubles that set out. We finalize describing an experience in the classroom and we extract some conclusions respect to supposing the incorporation of a subject oriented to solve a design using Bézier curves and surfaces.
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