Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

Document Type : Research Paper

Author

Faculty of Basic Sciences‎, ‎Department of Mathematics‎, ‎University of Zabol‎, ‎Zabol‎, ‎Iran.

Abstract

‎We present some inequalities for operator space numerical radius of $2\times 2$ block matrices on the matrix space $\mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

Keywords

Main Subjects

References

K.E. Gustafson and D.K.M. Rao, Numerical range, The field of values of linear operators and matrices, Universitext, Springer-Verlag, New York, 1997.
O. Hirzallah, F. Kittaneh and K. Shebrawi, Numerical radius inequalities for certain 2×2 operator matrices, Integral Equations Operator Theory 71 (2011), no. 1, 129--147.
F. Kittaneh, M.S. Moslehian and T. Yamazaki, Cartesian decomposition and numerical radius inequalities, Linear Algebra Appl. 471 (2015) 46--53.
T. Itoh and M. Nagisa, Numerical radius norms on operator spaces, J. Lond. Math. Soc. 74 (2006), no. 1, 154--166.
T. Itoh and M. Nagisa, Numerical radius Haagerup norm and square factorization through Hilbert spaces, J. Math. Soc. Japan 58 (2006), no. 2, 363--377.
M.S. Moslehian and M. Sattari, Inequalities for operator space numerical radius of 2×2 block matrices, J. Math. Phys. 57 (2016), Article ID 015201, 15 pages.
Z.J. Ruan, Subspaces of C*-algebras, J. Funct. Anal. 76 (1988), no. 1, 217--230.
M. Sattari, M.S. Moslehian and K. Shebrawi, Extension of Euclidean operator radius inequalities, Math. Scand. to appear.
M. Sattari, M.S. Moslehian and T. Yamazaki, Some generalized numerical radius inequalities for Hilbert space operators, Linear Algebra Appl. 470 (2015), no 1, 216--227.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 5
October 2017
Pages 1281-1285

Files

History

  • Receive Date: 02 January 2016
  • Revise Date: 21 May 2016
  • Accept Date: 22 May 2016

Share

How to cite

Statistics