Solution of a tridiagonal operator equation
نویسندگان
چکیده
Let H be a separable Hilbert space with an orthonormal basis {en/n ∈ N}, T be a bounded tridiagonal operator on H and Tn be its truncation on span ({e1, e2, . . . , en}). We study the operator equation T x = y through its finite dimensional truncations Tnx = yn. It is shown that if {‖T−1 n en‖} and {‖T ∗−1 n en‖} are bounded, then T is invertible and the solution of T x = y can be obtained as a limit in the norm topology of the solutions of its finite dimensional truncations. This leads to uniform boundedness of the sequence {T−1 n }. We also give sufficient conditions for the boundedness of {‖T−1 n en‖} and {‖T ∗−1 n en‖} in terms of the entries of the matrix of T . © 2005 Elsevier Inc. All rights reserved. AMS classification: Primary: 47B37; Secondary: 15A60, 65F99
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تاریخ انتشار 2006