Certain notes on the numerical range of an unbounded operator
A. Torgašev (1975)
Matematički Vesnik
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A. Torgašev (1975)
Matematički Vesnik
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Antonio J. Guirao, Olena Kozhushkina (2013)
Studia Mathematica
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We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).
Mohammad Ali Ardalani (2014)
Studia Mathematica
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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.
Jaćimovski, S.K., Ilić, D.I., Junger, I.K., Šetrajčić, J.P. (2001)
Novi Sad Journal of Mathematics
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Fuad Kittaneh (2005)
Studia Mathematica
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It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained. ...
Anita Dobek (2008)
Discussiones Mathematicae Probability and Statistics
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Debnath, Lokenath, Verma, Ram (1991)
International Journal of Mathematics and Mathematical Sciences
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E. Cancès, S. Labbé (2012)
ESAIM: Proceedings
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M. Życzkowski (1965)
Applicationes Mathematicae
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Dostál, Michal
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Mohammed Al-Dolat, Khaldoun Al-Zoubi, Mohammed Ali, Feras Bani-Ahmad (2016)
Open Mathematics
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Z. Kowalski (1963)
Annales Polonici Mathematici
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Takeaki Yamazaki (2007)
Studia Mathematica
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We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.
María D. Acosta (1990)
Extracta Mathematicae
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Křížek, Michal
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