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Absolutely bounded matrices and unconditional convergence
Author(s):
Milan
Hladnik
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3503-3511.
MSC (2000):
Primary 47B49;
Secondary 47L20
Posted:
June 10, 2008
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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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- 2.
- J. Diestel, H. Jarchow, A. Tonge, Absolutely summing operators, Cambridge University Press, 1995. MR 1342297 (96i:46001)
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- L. Livshits, S.-C. Ong, S.-W. Wang, Banach space duality of absolute Schur algebras, Integral Equations Operator Theory 41 (2001), 343-359. MR 1853675 (2002f:46087)
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- I. Schur, Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen, J. Reine Angew. Math. 140 (1911), 1-28.
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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
DOI:
10.1090/S0002-9939-08-09535-X
PII:
S 0002-9939(08)09535-X
Keywords:
Absolutely bounded matrices,
standard decomposition,
unconditional convergence,
absolutely compact matrices,
duality.
Received by editor(s):
June 13, 2007
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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