A Note on a Support of a Linear Mapping
A Note on a Theorem of A. D. Alexandroff
A note on Alexander's theorem.
A note on almost strong liftings
Let be a locally compact space. A lifting of where is a positive measure on , is almost strong if for each bounded, continuous function , and coincide locally almost everywhere. We prove here that the set of all measures on such that there exists an almost strong lifting of is a band.
A note on Banach spaces and sub differentials of convex functions
A note on copies of in spaces of weak* measurable functions
If is a finite measure space and a Banach space, in this note we show that , the Banach space of all classes of weak* equivalent -valued weak* measurable functions defined on such that a.e. for some equipped with its usual norm, contains a copy of if and only if contains a copy of .
A Note on Differentiability of Lipschitz Maps
We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
A note on geometric characterization of Fréchet differentiability
A note on global implicit function theorem.
A note on intermediate differentiability of Lipschitz functions
Let be a Lipschitz function on a superreflexive Banach space . We prove that then the set of points of at which has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces ), but it is even -porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.
A note on partial derivatives of convex functions
A note on polynomials versions
A note on singular points of convex functions in Banach spaces
A Note on Smoothability in Banach Spaces.
A note on the construction of measures taking their values in a Banach space with basis.
If E is a Banach space with a basis {en}, n belonging to N, a vector measure m: a --> E determines a sequence {mn}, n belonging to N, of scalar measures on a named its components. We obtain necessary and sufficient conditions to ensure that when given a sequence of scalar measures it is possible to construct a vector valued measure whose components were those given. Furthermore we study some relations between the variation of the measure m and the variation of its components.
A note on the extension of weak Radon measures on locally convex spaces to strong Radon measures
A one-sided version of Alexiewicz-Orlicz's differentiability theorem.
Modificando adecuadamente el método de un trabajo olvidado [1], probamos que si una aplicación continua, de un subconjunto abierto no vacío U de un espacio vectorial topológico metrizable separable y de Baire E, en un espacio localmente convexo, es direccionalmente diferenciable por la derecha en U según un subconjunto comagro de E, entonces, es genéricamente Gâteaux diferenciable en U. Nuestro resultado implica que cualquier espacio vectorial topológico, metrizable, separable y de Baire, es débilmente...
A Perron-type integral of order for Riesz spaces
A Pettis-type integral and applications to transition semigroups
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators....
A polynomial of degree four not satisfying Rolle’s Theorem in the unit ball of
We give an example of a fourth degree polynomial which does not satisfy Rolle’s Theorem in the unit ball of .