Absolutely bounded matrices and unconditional convergence

Hladnik, Milan

doi:10.1090/S0002-9939-08-09535-X

Absolutely bounded matrices and unconditional convergence
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Proc. Amer. Math. Soc. 136 (2008), 3503-3511 Request permission

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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