On -nearly uniform convex property in generalized Cesàro sequence spaces.
On property (β) of Rolewicz in Köthe-Bochner sequence spaces
We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve...
On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
On some convexity properties of generalized Cesàro sequence spaces.
On some expressions for the Riesz angles of Orlicz sequence spaces.
On some generalized -difference Riesz sequence spaces and uniform Opial property.
On some geometrical properties of generalized modular spaces of Cesàro type defined by weighted means. (On some geometrical properties of generalized modular spaces of Cesáro type defined by weighted means.)
On some local geometry of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm
Criteria for strong U-points, compactly locally uniformly rotund points, weakly compactly locally uniformly rotund points and locally uniformly rotund points in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm are given.
On some seminormed sequence spaces defined by a modulus function
On the compactness of the natural tensor product of compact operators.
On the distribution of random variables corresponding to Musielak-Orlicz norms
Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then , where is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM’(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the -norm by an arbitrary N-norm. This...
On the generalized -Riesz difference sequence space and -property.
On the -property of some Banach sequence spaces
In this paper we define a generalized Cesàro sequence space and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that the space posses property (H) and property (G), and it is rotund, where is a bounded sequence of positive real numbers with for all .
On the representation of uncountable symmetric basic sets and its applications
It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.
On the sets of sequences that are strongly -bounded and -convergent to naught with index .
On the space of -summable sequences
On the structure of the set of higher order spreading models
We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if is uncountable, then it contains an antichain of size...
On the λ-property and spaces of convergent sequences.
On Two Classes of Mappings on Banach Sequenee Spaces.
On uniform Kadec–Klee properties and rotundity in generalized Cesàro sequence spaces.