Solution of a tridiagonal operator equation

Balasubramanian, R. ; Kulkarni, S. H. ; Radha, R. (2006) Solution of a tridiagonal operator equation Linear Algebra and its Applications, 414 (1). pp. 389-405. ISSN 0024-3795

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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 Tx = y through its finite dimensional truncations Tnxn = yn. It is shown that if {||T−1nen||}and{||T∗−1nen||} are bounded, then T is invertible and the solution of Tx = 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−1n}. We also give sufficient conditions for the boundedness of {||T−1nen||} and {||T∗−1nen||} in terms of the entries of the matrix of T.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Diagonal Dominance; Determinant; Gerschgorin Disc; Tridiagonal Matrix; Tridiagonal Operator
ID Code:1289
Deposited On:04 Oct 2010 07:55
Last Modified:16 May 2016 12:26

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