On S$_1$-strictly singular operators
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- by Edward Odell and Ricardo V. Teixeira PDF
- Proc. Amer. Math. Soc. 143 (2015), 4745-4757 Request permission
Abstract:
Let $X$ be a Banach space and denote by $SS_1(X)$ the set of all S$_1$-strictly singular operators $T: X \longrightarrow X$. We prove that there is a Banach space $X$ such that $SS_1(X)$ is not an ideal. More specifically, we construct spaces $X$ and operators $T_1, T_2 \in SS_1(X)$ such that $T_1 + T_2 \notin SS_1(X)$. We show one example where the space $X$ is reflexive and another where it is $c_0$-saturated.References
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Additional Information
- Ricardo V. Teixeira
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas
- Address at time of publication: Department of Mathematics, University of Houston-Victoria, Victoria, Texas
- Email: teixeirar@uhv.edu
- Received by editor(s): September 25, 2013
- Received by editor(s) in revised form: January 15, 2014
- Published electronically: July 30, 2015
- Additional Notes: Edward Odell (1947–2013). The author passed away during the production of this paper.
This work is the main result of the second author’s Ph.D. thesis which was written under the supervision of the first author at the University of Texas at Austin - Communicated by: Thomas Schlumprecht
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4745-4757
- MSC (2010): Primary 46B03, 46B25, 46B28, 46B45, 47L20
- DOI: https://doi.org/10.1090/proc/12452
- MathSciNet review: 3391033
Dedicated: In Memoriam of Professor Ted Odell