Necessary results for spectral theory associated with the numerical range on Hilbert spaces
Abstract
This article examines aspects of the coupled numerical range for a linear
relation and a linear operator on Hilbert spaces. First of all, we start
by giving the new definition of this concept, and we study its properties.
Additionally, necessary results for the spectral theory associated with the
numerical range are discussed
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References
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relations involving SVEP. Mediterr. J. Math. 18, no. 2, Paper No. 77, 27 pp,
(2021).
[2] A. Ammar, A. Bouchekoua and N. Lazrag, Aiena’s local spectral theory for a
block matrix linear relations through localized SVEP, Rendiconti del Circolo
Matematico di Palermo Series 2(2022). https://doi.org/10.1007/s12215-021-
00699-3.
[3] A. Ammar, A. Jeribi and N. Lazrag, Sequence of multivalued linear operators
converging in the generalized sense. Bull. Iranian Math. Soc. 46, no. 6, 1697-
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[6] F. Kittaneh, Numerical radius inequalities for Hilbert space operators. Studia
Math. 168 , no. 1, 73–80, (2005).
[7] A. Abu-Omar and F. Kittaneh, Notes on some spectral radius and numerical
radius inequalities. Studia Math. 227, no. 2, 97–109, (2015).
[8] E. K. Gustafson and R. K. M. Duggirala, Numerical range. The field of
values of linear operators and matrices. Universitext. Springer-Verlag, New
York, xiv+189 pp. ISBN: 0-387-94835-X, (1997).
15
[9] T. Kato, Perturbation theory for linear operators. Reprint of the 1980 edition. Classics in Mathematics. Springer-Verlag, Berlin, xxii+619 pp. ISBN:
3-540-58661-X, (1995)
relations involving SVEP. Mediterr. J. Math. 18, no. 2, Paper No. 77, 27 pp,
(2021).
[2] A. Ammar, A. Bouchekoua and N. Lazrag, Aiena’s local spectral theory for a
block matrix linear relations through localized SVEP, Rendiconti del Circolo
Matematico di Palermo Series 2(2022). https://doi.org/10.1007/s12215-021-
00699-3.
[3] A. Ammar, A. Jeribi and N. Lazrag, Sequence of multivalued linear operators
converging in the generalized sense. Bull. Iranian Math. Soc. 46, no. 6, 1697-
1729, (2020).
[4] R. Arens, Operational calculus of linear relations. Pacific J. Math. 11, 9-23,
(1961).
[5] R. Cross, Multivalued linear operators. Monographs and Textbooks in Pure
and Applied Mathematics, 213. Marcel Dekker, Inc., New York, x+335 pp.
ISBN: 0-8247-0219-0, (1998).
[6] F. Kittaneh, Numerical radius inequalities for Hilbert space operators. Studia
Math. 168 , no. 1, 73–80, (2005).
[7] A. Abu-Omar and F. Kittaneh, Notes on some spectral radius and numerical
radius inequalities. Studia Math. 227, no. 2, 97–109, (2015).
[8] E. K. Gustafson and R. K. M. Duggirala, Numerical range. The field of
values of linear operators and matrices. Universitext. Springer-Verlag, New
York, xiv+189 pp. ISBN: 0-387-94835-X, (1997).
15
[9] T. Kato, Perturbation theory for linear operators. Reprint of the 1980 edition. Classics in Mathematics. Springer-Verlag, Berlin, xxii+619 pp. ISBN:
3-540-58661-X, (1995)
Published
2025-12-05
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