b-property on Riesz spaces and b-weakly compact operators

b-PROPERTY ON RİESZ SPACES and b-WEAKLY COMPACT OPERATORS (Ph.D.Thesis) BIROL ALTIN GAZI UNIVERSITY INSTUTE OF SCIENCE AND TECHNOLOGY August 2002 ABSTRACT In this thesis we define " b-property" on the Riezs spaces and we give some results about Riesz spaces which has b-property. When E is an AL-space and F is a Banach lattice with b-property, it is seen that each continous operator from E into F is order bounded; that is the equality L(E,F) = Xb(E,F) holds. We discuss the question "when does a cartesian product and a quotient of Riesz spaces has the b-property". In the last part of this thesis we define the classes of b-weakly compact operators. And we give a characterization about this kind of operators. Also some properties are found about b-weakly compact operators. Science Code : 403.03.01 Key words : b-property, b-order bounded set, b-weakly compact operator Page number : 65 Adviser : Yrd.Doç.Dr. Çevriye TONYALI