Some Properties of b-Weakly Compact Operators on Banach lattice

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. We present a necessary and sufficient condition under which each positive semi-compact operator is b-weakly compact.

• Na Cheng
• Zi-li Chen

• b-weakly compact
• Dunford-Pettis operator
• M-weakly compact operator
• L-weakly compact operator
• semi-compact operator
• weakly sequentially continuous lattice operations
• order continuous norm
• positive Schur property.

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