"On L and M-Weakly Compact Operators on Banach Lattices"
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
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.