Simultaneous solutions of operator Sylvester equations

Sang-Gu Lee; Quoc-Phong Vu

Studia Mathematica, Tome 223 (2014), p. 87-96 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Publié le : 2014-01-01

Zbl 1302.47028

EUDML-ID : urn:eudml:doc:285507

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     title = {Simultaneous solutions of operator Sylvester equations},
     journal = {Studia Mathematica},
     volume = {223},
     year = {2014},
     pages = {87-96},
     zbl = {1302.47028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm222-1-6}
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Sang-Gu Lee; Quoc-Phong Vu. Simultaneous solutions of operator Sylvester equations. Studia Mathematica, Tome 223 (2014) pp. 87-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm222-1-6/