Upper and lower bounds for numerical radii of block shifts


1 Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan.

2 Department of Mathematics, National Central University, Chun-gli 32001, Taiwan.


For 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.


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