Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

New operator inequalities in finite-dimensional vector spaces


Author: Alexander Y. Gordon
Journal: Proc. Amer. Math. Soc. 143 (2015), 4613-4622
MSC (2010): Primary 15A45, 47A63; Secondary 39A70
DOI: https://doi.org/10.1090/proc/12605
Published electronically: July 1, 2015
MathSciNet review: 3391021
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We establish some new operator inequalities in an $ n$-dimensional vector space $ X$ equipped with a seminorm $ \Vert\cdot \Vert$. Here is an example. If $ A$ is an invertible linear operator in $ X$ and $ \xi $ is a vector, then

$\displaystyle \Vert\xi \Vert^r \le \sum _{1\le \vert j\vert\le {n+r-1\choose r}}\Vert A^j\xi \Vert^r.$

Some special cases have been known and used in mathematical physics.

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

  • [1] H. L. Cycon, R. G. Froese, W. Kirsch, B. Simon. Schrödinger Operators with Application to Quantum Mechanics and Global Geometry. Springer, corrected edition: Berlin, 2007.
  • [2] David Damanik, Gordon-type arguments in the spectral theory of one-dimensional quasicrystals, Directions in mathematical quasicrystals, CRM Monogr. Ser., vol. 13, Amer. Math. Soc., Providence, RI, 2000, pp. 277–305. MR 1798997
  • [3] A. Ya. Gordon, A sufficient condition for continuity of the spectrum of a discrete Schrödinger operator, Funktsional. Anal. i Prilozhen. 20 (1986), no. 4, 70–71 (Russian). MR 878048
  • [4] Alexander Y. Gordon, Imperfectly grown periodic medium: absence of localized states, J. Spectr. Theory 5 (2015), no. 2, 279–294. MR 3355452, https://doi.org/10.4171/JST/98
  • [5] S. Jitomirskaya, Wen-Cai Liu. Arithmetic spectral transitions for the Maryland model, Preprint, 2014.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 15A45, 47A63, 39A70

Retrieve articles in all journals with MSC (2010): 15A45, 47A63, 39A70


Additional Information

Alexander Y. Gordon
Affiliation: Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, North Carolina 28223
Email: aygordon@uncc.edu

DOI: https://doi.org/10.1090/proc/12605
Received by editor(s): July 21, 2014
Published electronically: July 1, 2015
Communicated by: Michael Hitrik
Article copyright: © Copyright 2015 American Mathematical Society