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