Gap Between Operator Norm and Spectral Radius for the Square of Antidiagonal Block Operator Matrices
Abstract
In this work, the gap between operator norm and spectral radius for the square of antidiagonal block operator matrices in the direct sum of Banach spaces has been investigated, and also the gap between operator norm and numerical radius for the square of same matrices in the direct sum of Hilbert spaces has been studied.
Keywords
Antidiagonal operator matrix, Numerical radius, Operator norm, Spectral radius
References
- [1] P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York, 1982.
- [2] K. E. Gustafson, D. K. M. Rao, Numerical Range: The field of values of linear operators and matrices, Springer-Verlag, New York, 1982.
- [3] F. Kittaneh, Spectral radius inequalities for Hilbert space operators, Proc. Am. Math. Soc., 134(2) (2006), 385-390.
- [4] A. Abu-Omar, F. Kittaneh, Estimates for the numerical radius and spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials, Ann. Func. Anal., 5(1) (2014), 56-62.
- [5] A. Abu-Omar, F. Kittaneh, Upper and lower bounds for the numerical radius with an application to involution operators, Rocky Mt. J. Math., 45(4) (2015), 1055-1065.
- [6] A. Abu-Omar, F. Kittaneh, Notes on some spectral radius and numerical radius inequalities, Studia Math., 227(2) (2015), 97-109.
- [7] H. Guelfen, F. Kittaneh, On numerical radius inequalities for operator matrices, Numer. Funct. Anal. Optim., 40(11) (2019), 1231-1241.
- [8] Y. Bedrani, F. Kittaneh, M. Sabbaheh, Numerical radii of accretive matrices, Linear Multilinear Algebra, 69(5) (2021), 957-970.
- [9] W. Bani-Domi, F. Kittaneh, Norm and numerical radius inequalities for Hilbert space operators, Linear Multilinear Algebra, 69(5) (2021), 934-945.
- [10] M. Zima, A theorem on the spectral-radius of the sum of 2 operators and its application, Bull. Aust. Math. Soc., 48(3) (1993), 427-434.
