|
Non-invertibility of certain almost Mathieu operators
Author(s):
R.
Balasubramanian;
S.
H.
Kulkarni;
R.
Radha
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2017-2018.
MSC (2000):
Primary 47B37;
Secondary 15A15
Posted:
November 30, 2000
MathSciNet review:
1825912
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is shown that the almost Mathieu operators of the type   where  is real and  is a rational multiple of  and  an orthonormal basis for a Hilbert space, is not invertible.
References:
- [1]
- J.Avron, P.H.M.V.Mouche and B.Simon, On the measure of the spectrum for the almost Mathieu equation, Com.Math. Phys. (132) 1990, 103-118. MR 92d:39014a
- [2]
- J.Bellisard, R.Lima and D.Testand, Cantor spectrum for the almost Mathieu equation, J.Funct. Anal. (48) 1982, 408-419. MR 84h:81019
- [3]
- S.Jitomirskaya and Y. Last, Anderson Localization, continuity of gaps and measure of the spectrum, Comm. Math. Phys. (195) 1998, 1-14. MR 99j:81038
- [4]
- Y.Last, Almost everything about the almost Mathieu operator, Proceedings of XI international congress of Math. Physics, Paris, 1994, Intl. Press (1995), 366-372. MR 96m:82034
- [5]
- Y.Last, Zero measure spectrum for the almoist Mathieu operator, Comm. Math. Phys. (164) 1994, 421-432. MR 95f:47096
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
47B37,
15A15
Retrieve articles in all Journals with
MSC (2000):
47B37,
15A15
Additional Information:
R.
Balasubramanian
Affiliation:
The Institute of Mathematical Sciences, C.I.T. Campus, Madras-600 113, India
Email:
balu@imsc.ernet.in
S.
H.
Kulkarni
Affiliation:
Department of Mathematics, Indian Institute of Technology, Madras-600 036, India
Email:
shk@acer.iitm.ernet.in
R.
Radha
Affiliation:
Department of Mathematics, Anna University, Madras-600 025, India
Email:
radharam@annauniv.edu, radharam@imsc.ernet.in
DOI:
10.1090/S0002-9939-00-05760-9
PII:
S 0002-9939(00)05760-9
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
Posted:
November 30, 2000
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2000,
American Mathematical Society
|
