Maximizing numerical radii of weighted shifts under weight permutations

作者：Chang Chi Tung; Wang Kuo Zhong^*

来源：Journal of Mathematical Analysis and Applications, 2012, 394(2): 592-602.

DOI：10.1016/j.jmaa.2012.04.039

• Numerical range
• Numerical radius
• Weighted cyclic matrix
• Unilateral weighted shift
• Bilateral weighted shift

Let omega(i) is an element of C (1 %26lt;= i %26lt;= n) and I is an element of S-n, the symmetric group of all permutations of 1, 2,...,n. Suppose A(I) is the weighted cyclic matrix %26lt;br%26gt;[GRAPHICS] %26lt;br%26gt;and omega(A(I)) denotes its numerical radius. We characterize those zeta is an element of S-n which satisfy omega(A(zeta)) = max(vertical bar is an element of Sn) omega(A(I)). The characterizations for unilateral and bilateral weighted (backward) shifts are also obtained.

• 出版日期2012-10-15