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Non-invertibility of certain almost Mathieu operators

Authors: R. Balasubramanian, S. H. Kulkarni and R. Radha
Journal: Proc. Amer. Math. Soc. 129 (2001), 2017-2018
MSC (2000): Primary 47B37; Secondary 15A15
Published electronically: November 30, 2000
MathSciNet review: 1825912
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It is shown that the almost Mathieu operators of the type $Te_n~=$ $e_{n-1}+\lambda sin(2nr)e_n+e_{n+1}$where $\lambda$ is real and $r$ is a rational multiple of $\pi$and $\{e_n:n=1,2,3,...\},$ an orthonormal basis for a Hilbert space, is not invertible.

References [Enhancements On Off] (What's this?)

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Additional Information

R. Balasubramanian
Affiliation: The Institute of Mathematical Sciences, C.I.T. Campus, Madras-600 113, India

S. H. Kulkarni
Affiliation: Department of Mathematics, Indian Institute of Technology, Madras-600 036, India

R. Radha
Affiliation: Department of Mathematics, Anna University, Madras-600 025, India

Keywords: Almost Mathieu operator, determinant, tridiagonal matrix, tridiagonal operator
Received by editor(s): June 18, 1999
Received by editor(s) in revised form: November 5, 1999
Published electronically: November 30, 2000
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society

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