Solution of a tridiagonal operator equation |
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Authors: | R Balasubramanian R Radha |
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Institution: | a The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai 600 113, India b Department of Mathematics, Indian Institute of Technology, Chennai 600 036, India |
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Abstract: | 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 and 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 . We also give sufficient conditions for the boundedness of and in terms of the entries of the matrix of T. |
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Keywords: | Primary: 47B37 Secondary: 15A60 65F99 |
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