On the spectrum of the cesaro operator

Abstract

This thesis consists of four chapters. In chapter one, we determine the most general continuous linear functional f X, where X is any semiconservative BK-space with +) as its  Schauder basis. We also determine the necessary and sufficient conditions for(Ak)°bv°(X), bv(X), where Ak B(X, Y), X and Y are any Banach spaces.

In chapter two, we study the general FH-spaces with H = S, where S is the space of all double sequences in which coordinates are continuous. We then specialize and obtain the relation between c(c) , c(c), c(c) and RCN. We also prove that c(c) = RC.

In chapter three, we determine the spectrum of the Cesaro operator C1 = (C, 1) on c, bv, bv, wp (0) and wp (1p < ).

In chapter four, we study 4-dimensional matrices and then go on to determine the spectrum of the Cesaro operator C11 = (C, 1,1) on c(c) by a direct method. A method, which consists of both classical and analytical techniques.