A new approach to several results of V. Milman.
A new Approach to Temperate Generalized Colombeau Functions
A new approach to Young measure theory, relaxation and convergence in energy
A new characterization of Eberlein compacta
We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.
A new characterization of the interpolation spaces between L... and L...
A new characterization of the Sobolev space
The purpose of this paper is to provide a new characterization of the Sobolev space . We also show a new proof of the characterization of the Sobolev space , 1 ≤ p < ∞, in terms of Poincaré inequalities.
A New Characterization of Weighted Peetre K-Functionals (II)
2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented...
A new class of composition operators.
A new class of sequence spaces with applications in summability theory.
A new class of weakly countably determined Banach spaces
A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.
A new class of weakly -analytic Banach spaces
In this paper we define and investigate a new subclass of those Banach spaces which are -analytic in their weak topology; we call them strongly weakly -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not...
A new concept of separation
A new convexity property that implies a fixed point property for
In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result...
A new definition of nuclear systems with applications to bases in nuclear spaces
A New Dichotomy for Banach Spaces.
A new duality theory for compact groups.
A new Expression of the Maximal Value of Banach Limits
A new extension of Komlós' theorem in infinite dimensions. Application: Weak compactness in .
A new extension theorem for concave operators.