Abstract
In this note, we present several characterizations for some distinguished classes of bounded Hilbert space operators (self-adjoint operators, normal operators, unitary operators, and isometry operators) in terms of operator inequalities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Corach, R. Porta and L. Recht, An operator inequality, Linear Algebra Appl., 142 (1990), 153–158.
D. S. Djordjević and J.J. Koliha, Characterizing Hermitian, normal and EP operators, Filomat, 21 (2007), 39–54.
R.G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413–415.
J. Fujii, M. Fujii, T. Furuta and R. Nakamoto, Norm inequalities equivalent to Heinz inequality, Proc. Amer. Math. Soc., 118 (1993), 827–830.
E. Heinz, Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123 (1951), 415–438 (in German).
M. Mbekhta, Partial isometry and generalized inverses, Acta Sci. Math (Szeged), 70 (2004), 767–781.
A. Mcintosh, Heinz Inequalities and Perturbation of Spectral Families, Macquarie Mathematical Reports, Macquarie Univ., 1979.
S. Menkad, Partial isometries and norm equalities for operators, Matematicki Vesnik, 67 (2015), 269–276.
A. Seddik, Some results related to the Corach–Porta–Recht inequality, Proc. Amer. Math. Soc., 129 (2001), 3009–3015.
A. Seddik, On the injective norm and characterization of some subclasses of normal operators by inequalities or equalities, J. Math. Anal. Appl., 351 (2009), 277–284.
A. Seddik, Characterization of the class of unitary operators by operator inequalities, Linear Multilinear Algebra, 59 (2011), 1069–1074.
A. Seddik, Closed operator inequalities and open problems, Math. Inequal. Appl., 14 (2011), 147–157.
A. Seddik, Moore–Penrose inverse and operator inequalities, Extracta Math., 30 (2015), 29–39.
T. Yamazaka and M. Yanagida, Relations between two operator inequalities and their applications to paranormal operators, Acta Sci. Math. (Szeged), 69 (2003), 377–389.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L. Molnár
Rights and permissions
About this article
Cite this article
Bouraya, C., Seddik, A. On the characterizations of some distinguished subclasses of Hilbert space operators. ActaSci.Math. 84, 611–627 (2018). https://doi.org/10.14232/actasm-017-773-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.14232/actasm-017-773-6