Quaternionic Davis–Wielandt shell in a right quaternionic Hilbert space
Abstract
UDC 517.5
We derive some results concerning the quaternionic Davis–Wielandt shell for a bounded right linear operator in a right quaternionic Hilbert space. The relations between the geometric properties of the quaternionic Davis–Wielandt shells and the algebraic properties of quaternionic operators are obtained.
References
D. Alpay, F. Colombo, D. P. Kimsey, The spectral theorem for quaternionic unbounded normal operators based on the $S$-spectrum, J. Math. Phys., 57, № 2, Article 023503 (2016). DOI: https://doi.org/10.1063/1.4940051
M. T. Chien, H. Nakazato, Davis–Wielandt shell and $q$-numerical range, Linear Algebra and Appl., 340, 15–31 (2002). DOI: https://doi.org/10.1016/S0024-3795(01)00395-0
C. Davis, The shell of a Hilbert-space operator. II, Acta Sci. Math (Szeged), 31, 301–318 (1970).
F. Colombo, G. Gentili, I. Sabadini, D. C. Struppa, Non commutative functional calculus, bounded operators, Complex Anal. and Oper. Theory, 4, № 4, 821–843 (2010). DOI: https://doi.org/10.1007/s11785-009-0015-3
F. Colombo, I. Sabadini, On the formulations of the quaternionic functional calculus, J. Geom. and Phys., 60, № 10, 1490–1508 (2010). DOI: https://doi.org/10.1016/j.geomphys.2010.05.014
F. Colombo, J. Gantner, D. P. Kimsey, Spectral theory on the $S$-spectrum for quaternionic operators, Operator Theory: Adv. and Appl., 270, Birkhäuser/Springer (2018). DOI: https://doi.org/10.1007/978-3-030-03074-2
J. E. Jamison, Numerical range and numerical radius in quaternionic Hilbert space, Ph. D. Dissertation, Univ. Missouri (1972).
K. E. Gustafson, D. K. M. Rao, Numerical range, the field of values of linear operators and matrices, Springer, New York (1997). DOI: https://doi.org/10.1007/978-1-4613-8498-4_1
F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. Kyoto Univ., 24, 283–293 (1988). DOI: https://doi.org/10.2977/prims/1195175202
C. K. Li, N. K. Tsing, F. Uhlig, Numerical ranges of an operator on an indefinite inner product space, Electron. J. Linear Algebra, 1, 1–17 (1996). DOI: https://doi.org/10.13001/1081-3810.1000
C. K. Li, L. Rodman, Remarks on numerical ranges of operators in spaces with an indefinite metric, Proc. Amer. Math. Soc., 126, 973–982 (1998). DOI: https://doi.org/10.1090/S0002-9939-98-04242-7
A. Zamani, K. Shebrawi, Some upper bounds for the Davis–Wielandt radius of Hilbert space operators, Mediterr. J. Math., 17, № 1, 1–13 (2020). DOI: https://doi.org/10.1007/s00009-019-1458-z
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