Geodesic
A System of Operator Equations
Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 200-209

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DOI

Let be a separable Hilbert space, the algebra of all bounded operators on and Ai, Bi, ∊ , i = 1,. . . , r. It is shown that if no nontrivial linear combination of the operators A i, is compact, then there exist X, Y ∊ such that X Ai, Y = B i, for all i. A related (but much milder) result is discussed in other algebras with the unique maximal ideal and an application to elementary operators is given.
DOI : 10.4153/CMB-1987-029-2
Mots-clés : Primary 47A62, Secondary 16A53 
Magajna, Bojan. A System of Operator Equations. Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 200-209. doi: 10.4153/CMB-1987-029-2
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     title = {A {System} of {Operator} {Equations}},
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     year = {1987},
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     doi = {10.4153/CMB-1987-029-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-029-2/}
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