The search session has expired. Please query the service again.

Displaying similar documents to “Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space”

Inequalities for real number sequences with applications in spectral graph theory

Emina Milovanović, Şerife Burcu Bozkurt Altındağ, Marjan Matejić, Igor Milovanović (2022)

Czechoslovak Mathematical Journal

Similarity:

Let a = ( a 1 , a 2 , ... , a n ) be a nonincreasing sequence of positive real numbers. Denote by S = { 1 , 2 , ... , n } the index set and by J k = { I = { r 1 , r 2 , ... , r k } , 1 r 1 < r 2 < < r k n } the set of all subsets of S of cardinality k , 1 k n - 1 . In addition, denote by a I = a r 1 + a r 2 + + a r k , 1 k n - 1 , 1 r 1 < r 2 < < r k n , the sum of k arbitrary elements of sequence a , where a I 1 = a 1 + a 2 + + a k and a I n = a n - k + 1 + a n - k + 2 + + a n . We consider bounds of the quantities R S k ( a ) = a I 1 / a I n , L S k ( a ) = a I 1 - a I n and S k , α ( a ) = I J k a I α in terms of A = i = 1 n a i and B = i = 1 n a i 2 . Then we use the obtained results to generalize some results regarding Laplacian and normalized Laplacian eigenvalues of graphs.

Estimates of the principal eigenvalue of the p -Laplacian and the p -biharmonic operator

Jiří Benedikt (2015)

Mathematica Bohemica

Similarity:

We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet p -Laplacian and the Navier p -biharmonic operator on a ball of radius R in N and its asymptotics for p approaching 1 and . Let p tend to . There is a critical radius R C of the ball such that the principal eigenvalue goes to for 0 < R R C and to 0 for R > R C . The critical radius is R C = 1 for any N for the p -Laplacian and R C = 2 N in the case of the p -biharmonic operator. When p approaches 1 , the principal eigenvalue...

On the multiplicity of eigenvalues of conformally covariant operators

Yaiza Canzani (2014)

Annales de l’institut Fourier

Similarity:

Let ( M , g ) be a compact Riemannian manifold and P g an elliptic, formally self-adjoint, conformally covariant operator of order m acting on smooth sections of a bundle over M . We prove that if P g has no rigid eigenspaces (see Definition 2.2), the set of functions f C ( M , ) for which P e f g has only simple non-zero eigenvalues is a residual set in C ( M , ) . As a consequence we prove that if P g has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics...

Linear maps preserving A -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

Similarity:

Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there...

Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions

Catherine Bandle, Joachim von Below, Wolfgang Reichel (2008)

Journal of the European Mathematical Society

Similarity:

We consider linear elliptic equations - Δ u + q ( x ) u = λ u + f in bounded Lipschitz domains D N with mixed boundary conditions u / n = σ ( x ) λ u + g on D . The main feature of this boundary value problem is the appearance of λ both in the equation and in the boundary condition. In general we make no assumption on the sign of the coefficient σ ( x ) . We study positivity principles and anti-maximum principles. One of our main results states that if σ is somewhere negative, q 0 and D q ( x ) d x > 0 then there exist two eigenvalues λ - 1 , λ 1 such the positivity...

Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra

Ján Plavka (2016)

Kybernetika

Similarity:

A vector x is said to be an eigenvector of a square max-min matrix A if A x = x . An eigenvector x of A is called the greatest 𝐗 -eigenvector of A if x 𝐗 = { x ; x ̲ x x ¯ } and y x for each eigenvector y 𝐗 . A max-min matrix A is called strongly 𝐗 -robust if the orbit x , A x , A 2 x , reaches the greatest 𝐗 -eigenvector with any starting vector of 𝐗 . We suggest an O ( n 3 ) algorithm for computing the greatest 𝐗 -eigenvector of A and study the strong 𝐗 -robustness. The necessary and sufficient conditions for strong 𝐗 -robustness are introduced...