Absolutely bounded matrices and unconditional convergence
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Abstract:
We characterize the so-called absolutely bounded matrices in terms of the (strong) unconditional convergence of their standard decompositions. There is a similar characterization of absolutely compact matrices, and both characterizations are closely related to some natural multiplication operators. Rudiments of the duality theory for the algebra of all absolutely bounded matrices are included.References
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Additional Information
- Milan Hladnik
- Affiliation: University of Ljubljana, IMFM, Jadranska ul. 19, 1000 Ljubljana, Slovenia
- Email: milan.hladnik@fmf.uni-lj.si
- Received by editor(s): June 13, 2007
- Published electronically: June 10, 2008
- Additional Notes: This work was supported in part by the Ministry of Higher Education, Science and Technology of Slovenia.
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3503-3511
- MSC (2000): Primary 47B49; Secondary 47L20
- DOI: https://doi.org/10.1090/S0002-9939-08-09535-X
- MathSciNet review: 2415034