We prove that, under a mild condition on couple (A0,A1) of quasi-Banach spaces, all real interpolation spaces (A0,A1)?,p with 0<?<1 and 0<p?? are different from each other. In the Banach case for 1?p?? this was shown by Janson, Nilsson, Peetre Zafran, thus solving an old problem posed J.-L. Lions. Moreover, we give application to certain which important objects in Operator Theory consist bounde...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

We extend Troitsky’s ideas on measure-free martingales on Banach lattices to martingales of operators acting between a Banach lattice and a Banach space. We prove that each norm bounded martingale of cone absolutely summing (c.a.s.) operators (also known as 1-concave operators), from a Banach lattice E to a Banach space Y , can be generated by a single c.a.s. operator. As a consequence, we obta...

Many familiar and useful spaces of continuous or differentiable functions are Hilbert or Banach spaces, with pleasant completeness properties, but many are not. Some are Fréchet spaces, thus still complete, but lacking some of the conveniences of Banach spaces. Some other important spaces are not Fréchet, either. Still, some of these important spaces are colimits of Fréchet spaces (or of Banach...

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block q-Hilbertian and/or a block p-Besselian finite dimensional decomposition.

a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...