An important problem in Banach space theory since the 1950s has been the study of the structure of closed algebraic ideals in the algebra L (X ) where X is a Banach space.The Banach spaces X for which that structure is well-known are very few. It is known that every non-zero ideal in L (X ) contains the ideal of all finite-rank operators on X and that if X has a Schauder basis every non-zero closed ideal in L (X ) contains the ideal of all compact operators on X.In this dissertation I study the structure of the space (l_q)_c_0, for 1 \u3c q \u3c and I find the unique proper maximal ideal in the algebra L((l_q)_c_0).Let T be a bounded linear operator on X=(l_q)_c_0 with
