On some numerical representation of Post algebras
J. Klukowski, T. Traczyk (1977)
Colloquium Mathematicae
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J. Klukowski, T. Traczyk (1977)
Colloquium Mathematicae
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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.
Anita Dobek (2008)
Discussiones Mathematicae Probability and Statistics
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A. Torgašev (1975)
Matematički Vesnik
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E. Cancès, S. Labbé (2012)
ESAIM: Proceedings
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Dostál, Michal
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M. Życzkowski (1965)
Applicationes Mathematicae
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K. Urbanik (1966)
Fundamenta Mathematicae
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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.
Gneiting, Tilmann, Konis, Kjell, Richards, Donald (2001)
Experimental Mathematics
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Z. Kowalski (1963)
Annales Polonici Mathematici
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Křížek, Michal
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Mohammed Al-Dolat, Khaldoun Al-Zoubi, Mohammed Ali, Feras Bani-Ahmad (2016)
Open Mathematics
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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).
Wen Yan, Jicheng Tao, Zhao Lu (2016)
Special Matrices
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In this paper we studied the classical numerical range of matrices in sp(2n, C). We obtained some result on the relationship between the numerical range of a matrix in and that [...] of its diagonal block, the singular values of its off-diagonal block A2.