Simultaneous solutions of operator Sylvester equations

• Autorzy: Sang-Gu Lee , Quoc-Phong Vu
• Języki publikacji: EN

Abstrakty

EN

We consider simultaneous solutions of operator Sylvester equations $A_{i}X - XB_{i} = C_{i}$ (1 ≤ i ≤ k), where $(A₁,..., A_{k})$ and $(B₁,..., B_{k})$ are commuting k-tuples of bounded linear operators on Banach spaces 𝓔 and ℱ, respectively, and $(C₁,..., C_{k})$ is a (compatible) k-tuple of bounded linear operators from ℱ to 𝓔, and prove that if the joint Taylor spectra of $(A₁,..., A_{k})$ and $(B₁,..., B_{k})$ do not intersect, then this system of Sylvester equations has a unique simultaneous solution.

Kategorie tematyczne

• 15A24: Matrix equations and identities
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47A62: Equations involving linear operators, with operator unknowns
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 222
• Numer: 1
• Strony: 87-96

Daty

wydano

2014

Twórcy

autor

Sang-Gu Lee

• Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

autor

Quoc-Phong Vu

• Department of Mathematics, Ohio University, Athens, OH 45701, USA
• Vietnam Institute of Advanced Study in Mathematics, Hanoi, Vietnam

Identyfikatory

DOI

10.4064/sm222-1-6