On the finite dimensional orbits of linear operators
On the Fréchet differentiability of distance functions
On the generalized continuity of the semivariation in locally convex spaces
On the generalized Roper-Suffridge extension operator in Banach spaces.
On the geometric characterization of differentiability. I.
On the geometric characterization of differentiability. II.
On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with...
On the limitations of the Grothendieck techniques.
On the Mazur-Orlicz theorem
On the modulus of measures with values in topological Riesz spaces.
The paper is devoted to a study of some aspects of the theory of (topological) Riesz space valued measures. The main topics considered are the following. First, the problem of existence (and, particularly, the so-called proper existence) of the modulus of an order bounded measure, and its relation to a similar problem for the induced integral operator. Second, the question of how properties of such a measure like countable additivity, exhaustivity or so-called absolute exhaustivity, or the properties...
On the multiplicity points of monotone operators on separable Banach spaces
On the open mapping principle and convex multivalued mappings
On the product of operator valued measures
On the Projective Tensor Product of Vector-Valued Measures. II.
On the quasinormability of Hb (U).
On the radius of convergence of an entire function in a normed space
On the range of the derivative of a real-valued function with bounded support
We study the set f’(X) = f’(x): x ∈ X when f:X → ℝ is a differentiable bump. We first prove that for any C²-smooth bump f: ℝ² → ℝ the range of the derivative of f must be the closure of its interior. Next we show that if X is an infinite-dimensional separable Banach space with a -smooth bump b:X → ℝ such that is finite, then any connected open subset of X* containing 0 is the range of the derivative of a -smooth bump. We also study the finite-dimensional case which is quite different. Finally,...
On the range of the derivative of a smooth function and applications.
We survey recent results on the structure of the range of the derivative of a smooth real valued function f defined on a real Banach space X and of a smooth mapping F between two real Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of L(X,Y) for the existence of a Fréchet-differentiable mapping F from X into Y so that F'(X) = A. Whenever F is only assumed Gâteaux-differentiable, new phenomena appear: we discuss the existence of a mapping F...
On the range of the derivative of a smooth mapping between Banach spaces.
On the right inverse operators which are defined by Eidelheit sequences.