In this paper, we investigate the relationship between weak min-max property and diameter uniformity of domains in Banach spaces with dimension at least 2. As an application, show that uniform are invariant under relatively quasimöbius mappings.

We have introduced a new sequence space l(r,s,t, p;Δ(m) ) combining by using generalized means and difference operator of order m . Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α -, β -, γ duals of this space are computed and also obtained necessary and sufficient conditions for s...

Following Davie’s example of a Banach space failing the approximation property ([D]), we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is “almost” a weak Hilbert space and which can be written as the direct sum of two subspaces all of who...

The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive, and more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has an alike Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce t...

We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja’s conjecture. As a consequence, we show that each of the spaces c0 and `1 has a subspace which has the AP but fails to have the strong AP.

Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...