Geodesic
A note on compactness of tensor products
Carlos Kubrusly1 ; Joao Zanni1 ; Carlos Kubrusly ; Joao Zanni
1DEE - Catholic University, R. Marques de S. Vicente 225
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 59-62 
Carlos Kubrusly; Joao Zanni; Carlos Kubrusly; Joao Zanni. A note on compactness of tensor products. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 59-62. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a5/
@article{AMUC_2015_84_1_a5,
     author = {Carlos Kubrusly and Joao Zanni and Carlos Kubrusly and Joao Zanni},
     title = { A note on compactness of tensor products},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {59--62},
     year = {2015},
     volume = {84},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a5/}
}
TY  - JOUR
AU  - Carlos Kubrusly
AU  - Joao Zanni
AU  - Carlos Kubrusly
AU  - Joao Zanni
TI  - A note on compactness of tensor products
JO  - Acta mathematica Universitatis Comenianae
PY  - 2015
SP  - 59
EP  - 62
VL  - 84
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a5/
ID  - AMUC_2015_84_1_a5
ER  - 
%0 Journal Article
%A Carlos Kubrusly
%A Joao Zanni
%A Carlos Kubrusly
%A Joao Zanni
%T A note on compactness of tensor products
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 59-62
%V 84
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a5/
%F AMUC_2015_84_1_a5

Voir la notice de l'article provenant de la source Comenius University

Compactness is preserved from a pair of operators to their tensor product. The converse was considered in [10] 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.