Amer Abu Omar, Fuad Kittaneh (2013)
Studia Mathematica
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A spectral radius inequality is given. An application of this inequality to prove a numerical radius inequality that involves the generalized Aluthge transform is also provided. Our results improve earlier results by Kittaneh and Yamazaki.
Debnath, Lokenath, Verma, Ram (1991)
International Journal of Mathematics and Mathematical Sciences
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Mostafa Mbekhta, Jaroslav Zemánek (2007)
Banach Center Publications
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Irene Rousseau (2001)
Visual Mathematics
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Benalili, Mohammed, Lansari, Azzedine (2005)
Lobachevskii Journal of Mathematics
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Rakhmatullina, L.F. (1997)
Memoirs on Differential Equations and Mathematical Physics
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Lihua You, Yujie Shu, Xiao-Dong Zhang (2016)
Czechoslovak Mathematical Journal
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We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
P. A. Cojuhari, A. M. Gomilko (2008)
Studia Mathematica
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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.
Robert Grone, Peter D. Johnson, Jr. (1982)
Colloquium Mathematicae
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Peter D. Johnson, Jr. (1978)
Colloquium Mathematicae
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Tosio Kato (1982)
Mathematische Zeitschrift
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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. ...
M. T. Karaev (2006)
Colloquium Mathematicae
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Omar Hirzallah, Fuad Kittaneh, Khalid Shebrawi (2012)
Studia Mathematica
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We derive several numerical radius inequalities for 2 × 2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
Vlastimil Pták (1982)
Banach Center Publications
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Zagorodnyuk, S. M. (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.
Daniel Beltiţă (2001)
Studia Mathematica
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We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.