No abstract

Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.

Remark 4. In [8], the operator A with the nonlocal condition (2) was considered. It was assumed that conditions 1)-3) and 5) are satisfied, F2 = 6, and FI = OQ. Accordingly, in the cited example the following restrictions were imposed on the nonlocal conditions (3): ~ C Q and ws(OQ) c Q.The author thanks A. L. Skubachevskii for posing the problem and for his permanent interest in this work.

We investigate the duality and norm completeness in the classes of limitedly-L-weakly compact and Dunford-Pettis-L-weakly compact and operators from Banach spaces to Banach lattices.

We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We give its efficient characterization in term of sequences, investigate the domination problem, and study the completeness of this class of operators.