This is a Minority Research Initiative Planning Grant proposal. Since receiving his doctorate in 1980, the demands of teaching at a small minority liberal arts college have afforded little opportunity for Professor Robinson to pursue the research interests which he had so successfully developed in his doctoral work. For this reason, he is seeking funding support to renew his research efforts. He plans to initiate a research program that continues the investigations in his thesis in the area of operators on Banach space, specifically shift operators and notions of orthogonality. He will begin by extracting research publications from his dissertation, and submit them to mathematical journals. Later research will aim at further extensions of these results.