Norm closed ideals in the algebra of bounded linear operators on Orlicz sequence spaces
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- by Peikee Lin, Bünyamin Sarı and Bentuo Zheng PDF
- Proc. Amer. Math. Soc. 142 (2014), 1669-1680 Request permission
Abstract:
For each $1<p<\infty$, we consider a class of $p$-regular Orlicz sequence spaces $\ell _M$ that are “close” to $\ell _p$ and study the structure of the norm closed ideals in the algebra of bounded linear operators on such spaces. We show that the unique maximal ideal in $L(\ell _M)$ is the set of all $\ell _M$ strictly singular operators and the immediate successor of the ideal of compact operators in $L(\ell _M)$ is the closed ideal generated by the formal identity from $\ell _M$ into $\ell _p$.References
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Additional Information
- Peikee Lin
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- Email: peikee@memphis.edu
- Bünyamin Sarı
- Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
- MR Author ID: 741208
- Email: bunyamin@unt.edu
- Bentuo Zheng
- Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
- Email: bzheng@memphis.edu
- Received by editor(s): December 7, 2011
- Received by editor(s) in revised form: January 30, 2012, March 19, 2012, April 27, 2012, May 23, 2012, and June 11, 2012
- Published electronically: February 10, 2014
- Additional Notes: The research of the third author was partially supported by NSF DMS-1200370.
- Communicated by: Thomas Schlumprecht
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 1669-1680
- MSC (2010): Primary 47L20; Secondary 47B37, 47B10
- DOI: https://doi.org/10.1090/S0002-9939-2014-11903-4
- MathSciNet review: 3168473