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Proceedings of the American Mathematical Society

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Absolutely bounded matrices and unconditional convergence

Author: Milan Hladnik
Journal: Proc. Amer. Math. Soc. 136 (2008), 3503-3511
MSC (2000): Primary 47B49; Secondary 47L20
Published electronically: June 10, 2008
MathSciNet review: 2415034
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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.

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Milan Hladnik
Affiliation: University of Ljubljana, IMFM, Jadranska ul. 19, 1000 Ljubljana, Slovenia

Keywords: Absolutely bounded matrices, standard decomposition, unconditional convergence, absolutely compact matrices, duality.
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.