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 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |