On block diagonal majorization and basic sequences

In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using block diagonal row stochastic matrices (as a special case), we define the relation < bdr on c0, which is said block diagonal majorization. We also obtain some important properties of Pbdr, the set of all bounded linear operators T : c0 ? c0; which preserve < bdr : Further, it is obtained necessary conditions for a bounded linear operator T on c0 to be a preserver of the block diagonal majorization < bdr. Also, the notion of the basic sequences correspond to block diagonal row stochastic matrices with description of some relevant examples will be discussed.