**"****On L and M-Weakly Compact
Operators on Banach Lattices****"**

By

** Abstract:** A sequence (xn) in a Banach lattice is called disjoint if |xn| Λ|xm| = 0 whenever n≠ m. Disjoint sequences in Banach lattices enable us to
introduce L and M-weakly compact operators. A bounded operator T:E → X is called M-weakly compact if ||Txn|| → 0 for each norm bounded
disjoint sequence (xn) in the Banach lattice E. Duals of M-weakly compact
operators are called L-weakly compact operators. We give characterizations of M
and L-weakly compact operators. We identify further properties of these classes
of operators. We study the relations between these classes and others such as
semicompact, Dunford-Pettis, weak Dunford-Pettis, almost Dunford-Pettis and
finite rank operators.

**Date: ****Wednesday, April 17, 2013**

**Time: ****14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.