L-weakly compact and M-weakly compact operators

11 L-WEAKLY AND M-WEAKLY COMPACT OPERATORS (M.Sc. Thesis) Erdal BAYRAM GAZI UNIVERSTY INSTUTE OF SCIENCE AND TECHNOLOGY August 2002 ABSTRACT In this thesis work we have studied the paper written by Z.L. Chen-A.W. Wickstead: "L-wakly and M-weakly compact operators". They answered the following questions : (Q1) If T:E-»F is a L-weakly compact operator (M-weakly compact), does it imply that T has a modulus? (Q2) If the modulus |T| does exist must it be L-weakly compact (M-weakly compact) ? (Q3) When are regular M-weakly compact operators L-weakly compact and viceversa? In the present work, we have collected the necessary definitions, theorems and results about the subject We have given detailed proofs of their theorems. Science Code : 403.03.01 Key Words : O-weakly compact operator, L-weakly compact operator, M-weakly compact operator Page Number : 114 Adviser : Yrd.Doc.Dr. Çevriye Tonyalı