We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

Let E be an ideal of Lo over a σ-finite measure space (Ω,Σ, μ), and let (X, ‖ ·‖X) be a real Banach space. Let E(X) be a subspace of the space Lo(X) of μ-equivalence classes of all strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ Lo(X) for which the scalar function ‖f(·)‖X belongs to E. Let E(X)n stand for the order continuous dual of E(X). In this paper we characteriz...

In this brief note, we prove that every space is a sequence-covering image of a topological sum of convergent sequences. As the application of this result, sequence-covering images of locally compact metric spaces (or, locally separable metric spaces, metric spaces) and sequentially-quotient images of a locally compact metric spaces (or, locally separable metric spaces, metric spaces) are equiv...

We demonstrate a proof-of-concept optical spectroscopic system for bioaerosol-particle fluorescence detection, in which a pulsed high-power laser is replaced by a highly compact linear array of sequentially fired light from blue light-emitting diodes. The results suggest that low-cost, compact optical aerosol detection may be feasible with the contemporary emergence of efficient UV light-emitti...

We compare two constructions of families of sequentially compact Ilausdorff spaces whose product is not countably compact, and show that every space that can be constructed by one construction is homeomorphic to a subspace of some space constructed by the other construction, but not vice versa.

We show that the image of a commutative monotone sequentially complete C∗-algebra, under a sequentially normal morphism, is again a monotone sequentially complete C-algebra, and also a monotone sequentially closed C∗-subalgebra. As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed. In the case of a un...

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.