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A linear operator between two ordered vector spaces that carries positive elements to positive elements is known in the literature as a positive operator. As we have mentioned in the preface, the main theme of this book is the study of positive operators. To obtain fruitful and useful results the domains and the ranges of positive operators will be taken to be Riesz spaces (vector lattices). For this reason, in order to make the material as self-sufficient as possible, the fundamental properties of Riesz spaces are discussed as they are needed.

A compact operator sends an arbitrary norm bounded sequence to a sequence with a norm convergent subsequence. For this reason, when operators are associated with integral equations, the compact operators are the most desirable. Besides being compact, an operator with some type of compactness is more useful than an arbitrary operator.

It is well known that most classical Banach spaces are, in fact, Banach lattices on which positive operators appear naturally. This chapter is devoted to the study of Banach lattices with special emphasis on Banach lattices with order continuous norms.

It is well known that most classical Banach spaces are, in fact, Banach lattices on which positive operators appear naturally. This chapter is devoted to the study of Banach lattices with special emphasis on Banach lattices with order continuous norms.

It is well known that most classical Banach spaces are, in fact, Banach lattices on which positive operators appear naturally. This chapter is devoted to the study of Banach lattices with special emphasis on Banach lattices with order continuous norms.

It is well known that most classical Banach spaces are, in fact, Banach lattices on which positive operators appear naturally. This chapter is devoted to the study of Banach lattices with special emphasis on Banach lattices with order continuous norms.

It is well known that most classical Banach spaces are, in fact, Banach lattices on which positive operators appear naturally. This chapter is devoted to the study of Banach lattices with special emphasis on Banach lattices with order continuous norms.

It is well known that operator theory is intrinsically related to the topological structures associated with the spaces upon which the operators act. The theory of positive operators is no exception to this phenomenon. The various topological notions provide an invaluable insight into the properties of operators. This chapter is devoted to the basic topological concepts needed for the study of positive operators. The presentation (although concise) is quite complete. The discussion focuses on locally convex spaces, Banach spaces, and locally solid Riesz spaces.