in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

‎let $x$‎, ‎$y$ and $z$ be banach spaces and $f:xtimes y‎ ‎longrightarrow z$ a bounded bilinear map‎. ‎in this paper we‎ ‎study the relation between arens regularity of $f$ and the‎ ‎reflexivity of $y$‎. ‎we also give some conditions under which the‎ ‎arens regularity of a banach algebra $a$ implies the arens‎ ‎regularity of certain banach right module action of $a$‎ .

The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general Lp-spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banac...

This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the Hahn-Banach theorem is proven. The separation problem is considered in linear topological spaces, locally convex linear topological spaces, Banach spaces, and finally finite dimensional Banach spaces. A n...

1. Editor’s note 1 2. Research announcements 2 2.1. Lecce Workshop presentations available online 2 2.2. Borel cardinalities below c0 2 2.3. Hereditarily non-topologizable groups 2 2.4. A hodgepodge of sets of reals 2 2.5. Random gaps 3 2.6. Covering a bounded set of functions by an increasing chain of slaloms 3 2.7. Baire-one mappings contained in a usco map 3 2.8. Applications of k-covers II ...

1. Non-Banach limits C(R), C∞(R) of Banach spaces C[a, b] 2. Banach completion C o (R) of C c (R) 3. Rapid-decay functions, Schwartz functions 4. Non-Fréchet colimit C∞ c (R) of Fréchet spaces 5. LF-spaces of moderate-growth functions 6. Strong operator topology 7. Generalized functions (distributions) on R 8. Tempered distributions and Fourier transforms on R 9. Test functions and Paley-Wiener...

In [K.-I. Mitani and K.-S. Saito, J. Math. Anal. Appl. 327 (2007), 898–907] we characterized the strict convexity, uniform convexity and uniform non-squareness of Banach spaces using ψ-direct sums of two Banach spaces, where ψ is a continuous convex function with some appropriate conditions on [0, 1]. In this paper, we characterize the Bn-convexity and Jn-convexity of Banach spaces using ψ-dire...

We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space ΞB contained in the space of bounded Borel measures on T in such a way that the map B → ΞB defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of a...

The present thesis deals with computable functional analysis and in this context, especially, with compact operators on computable Banach spaces. For this purpose, the representation based approach to computable analysis (TTE) is used. In the first part, computable Banach spaces with computable Schauder bases are introduced and two representations each are defined for the dual space of a comput...

We investigate the existence of infinite dimensional Banach spaces having rigid sets with an infinite number of elements. Among Banach lattices, examples are provided by infinite dimensional AM -spaces as well as for some abstract Lp-spaces, 1 ≤ p < ∞.