In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space , when X is a numerical radius operator space. Moreover, we establish several inequalities for operator space numerical radius and the maximal numerical radius norm of 2 × 2 operator matrices and their off-diagonal parts. One of our main results states that if (X, (On)) is an operator space, then for all .
REFERENCES
1.
A.
Abu-Omar
and F.
Kittaneh
, “Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials
,” Ann. Funct. Anal.
5
(1
), 56
–62
(2014
).2.
M. D.
Choi
, D. W.
Kribs
, and K.
Zyczkowski
, “Quantum error correcting codes from the compression formalism
,” Rep. Math. Phys.
58
, 77
–91
(2006
).3.
E. G.
Effros
and Z.-J.
Ruan
, “Operator spaces
,” in London Mathematical Society Monographs
, New Series
Vol. 23
(The Clarendon Press, Oxford University Press
, New York
, 2000
).4.
K. E.
Gustafson
and D. K. M.
Rao
, “Numerical range
,” in The Field of Values of Linear Operators and Matrices. Universitext
(Springer-Verlag
, New York
, 1997
).5.
O.
Hirzallah
, F.
Kittaneh
, and K.
Shebrawi
, “Numerical radius inequalities for certain 2 × 2 operator matrices
,” Integral Equations Operator Theory
71
(1
), 129
–147
(2011
).6.
O.
Hirzallah
, F.
Kittaneh
, and K.
Shebrawi
, “Numerical radius inequalities for commutators of Hilbert space operators
,” Numer. Funct. Anal. Optim.
32
, 739
–749
(2011
).7.
T.
Itoh
and M.
Nagisa
, “Numerical radius norms on operator spaces
,” J. London. Math. Soc.
74
, 154
–166
(2006
).8.
T.
Itoh
and M.
Nagisa
, “Numerical radius Haagerup norm and square factorization through Hilbert spaces
,” J. Math. Soc. Japan
58
(2
), 363
–377
(2006
).9.
F.
Kittaneh
, M. S.
Moslehian
, and T.
Yamazaki
, “Cartesian decomposition and numerical radius inequalities
,” Linear Algebra Appl.
471
, 46
–53
(2015
).10.
C. K.
Li
and Y. T.
Poon
, “Generalized numerical ranges and quantum error correction
,” J. Operator Theory.
66
(2
), 335
–351
(2011
).11.
C. K.
Li
, Y. T.
Poon
, and N.-S.
Sze
, “Higher rank numerical ranges and low rank perturbations of quantum channels
,” J. Math. Anal. Appl.
348
(2
), 843
–855
(2008
).12.
Z.
Puchała
, J. A.
Miszczak
, P.
Gawron
, C. F.
Dunkl
, J. A.
Holbrook
, and K.
Zyczkowski
, “Restricted numerical shadow and the geometry of quantum entanglement
,” J. Phys. A
45
(41
), 415309
(2012
).13.
Z-J.
Ruan
, “subspaces of C∗-algebras
,” J. Funct. Anal.
76
, 217
–230
(1988
).14.
M.
Sattari
, M. S.
Moslehian
, and T.
Yamazaki
, “Some generalized numerical radius inequalities for Hilbert space operators
,” Linear Algebra Appl.
470
(1
), 216
–227
(2015
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
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