"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.