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Norm closed ideals in the algebra of bounded linear operators on Orlicz sequence spaces


Authors: Peikee Lin, Bünyamin Sarı and Bentuo Zheng
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
Published electronically: February 10, 2014
MathSciNet review: 3168473
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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$.


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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
Email: bunyamin@unt.edu

Bentuo Zheng
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Email: bzheng@memphis.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11903-4
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.