Simultaneous solutions of operator Sylvester equations
Sang-Gu Lee, Quoc-Phong Vu (2014)
Studia Mathematica
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We consider simultaneous solutions of operator Sylvester equations (1 ≤ i ≤ k), where and are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of and do not intersect, then this system of Sylvester equations has a unique simultaneous solution.