Invariant Subspaces for Certain Finite-rank Perturbations of Diagonal Operators
نویسندگان
چکیده
Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satisfy an `-condition with respect to the orthonormal basis {ek}, and if T is not a scalar multiple of the identity operator, then T has a non-trivial hyperinvariant subspace.
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