On log-subharmonicity of singular values of matrices

• Autorzy: Bernard Aupetit
• Języki publikacji: EN

Abstrakty

EN

Let F be an analytic function from an open subset Ω of the complex plane into the algebra of n×n matrices. Denoting by $s_1,...,s_n$ the decreasing sequence of singular values of a matrix, we prove that the functions $log s_{1}(F(λ)) + ... + log s_{k}(F(λ))$ and $log^{+}s_{1}(F(λ)) + ... + log^{+}s_{k}(F(λ))$ are subharmonic on Ω for 1 ≤ k ≤ n.

Kategorie tematyczne

• 31A05: Harmonic, subharmonic, superharmonic functions
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 2
• Strony: 195-200

Daty

wydano

1997

otrzymano

1996-06-28

Twórcy

autor

Bernard Aupetit

• Département de mathématiques et de statistique, Faculté des sciences et de génie, Université Laval, Québec, Canada, G1K 7P4

Bibliografia

• [1] B. Aupetit, A Primer on Spectral Theory, Springer, New York, 1991.
• [2] B. Aupetit et A. Iyamuremye, Sous-harmonicité de la partie de Riesz du spectre d'un opérateur, Ann. Sci. Math. Québec 12 (1988), 171-177.
• [3] H. König, Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel, 1986.
• [4] O. Nevanlinna, A characteristic function for matrix valued meromorphic functions, Helsinki University of Technology, Institute of Mathematics Research Report A 355, 1995.
• [5] O. Nevanlinna, Meromorphic resolvents and power bounded operators, Helsinki University of Technology, Institute of Mathematics Research Report A 358, 1996.