ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




A note on compactness of tensor products

J. Zanni and C. S. Kubrusly

Received: February 27, 2014;   Revised: March 11, 2014;   Accepted: March 19, 2014



Abstract.   Compactness is preserved from a pair of operators to their tensor product. The converse was considered in [13] under some restrictions on the spectra of the operators. This paper shows that no restriction is necessary: the converse holds whenever the tensor product is nonzero.

Keywords:  Tensor product; compact operators; compactness preservation.  

AMS Subject classification: Primary:  47A80;   Secondary: 47B07


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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