in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

Let X,Y be locally convex spaces and L(X,Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series P Tk in L(X,Y ). First, if λ is a scalar sequence space, we say that the series P Tk is λ multiplier convergent for a locally convex topology τ on L(X,Y ) if the series P tkTk is τ convergent for every t = {tk} ∈ λ. We establish...

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

In this paper we describe a family of open questions concerning strong completeness properties associated with the Baire Category Theorem. Some of our questions deal with classical completeness topics such as de Groot’s subcompactness property and the property now called Choquet completeness, while others ask about more recent topics such as domain-representability and its relation to classical...