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  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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