Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41Issue 7 (Special Issue)20151201Upper and lower bounds for numerical radii of block shifts1527719ENP. Y.WuDepartment of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.H.-L.GauDepartment of Mathematics, National Central University, Chun-gli 32001, Taiwan.Journal Article20140904For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine when either of them becomes an equality.http://bims.iranjournals.ir/article_719_7b89cecc3c9d266bd2d8a5e08a8dc1cb.pdf