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Simultaneous solutions of operator Sylvester equations

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Lee S.-G., Vu Q.-P.

Studia Mathematica

2014

tom 222

nr 1

87-96

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.

Ograniczanie wyników

1 Studia Mathematica

1 Lee S.-G.

1 Vu Q.-P.

1 2014

Wyniki wyszukiwania

Simultaneous solutions of operator Sylvester equations