Geodesic
Compact actions on C*-algebras
Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 143-149

Voir la notice de l'article provenant de la source Cambridge University Press

In Section 33 of [2], Bonsall and Duncan define an element t of a Banach algebra to act compactly on if the map a → tat is a compact operator on . In this paper, the arguments and technique of [1] are used to study this question for C*-algebras (see also [10]). We determine the elements b of a C*-algebra for which the maps a → ba, a → ab, a → ab + ba, a → bab are compact (respectively weakly compact), determine the C*-algebras which are compact in the sense of Definition 9, of [2, p. 177] and give a characterization of the C*-automorphisms of which are weakly compact perturbations of the identity. 
Akemann, Charles A.; Wright, Steve. Compact actions on C*-algebras. Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 143-149. doi: 10.1017/S0017089500004298
@article{10_1017_S0017089500004298,
     author = {Akemann, Charles A. and Wright, Steve},
     title = {Compact actions on {C*-algebras}},
     journal = {Glasgow mathematical journal},
     pages = {143--149},
     year = {1980},
     volume = {21},
     number = {2},
     doi = {10.1017/S0017089500004298},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004298/}
}
TY  - JOUR
AU  - Akemann, Charles A.
AU  - Wright, Steve
TI  - Compact actions on C*-algebras
JO  - Glasgow mathematical journal
PY  - 1980
SP  - 143
EP  - 149
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004298/
DO  - 10.1017/S0017089500004298
ID  - 10_1017_S0017089500004298
ER  - 
%0 Journal Article
%A Akemann, Charles A.
%A Wright, Steve
%T Compact actions on C*-algebras
%J Glasgow mathematical journal
%D 1980
%P 143-149
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004298/
%R 10.1017/S0017089500004298
%F 10_1017_S0017089500004298

[1] 1.Akemann, C. A. and Wright, S., Compact and weakly compact derivations of C*-algebras, Pacific J. Math., to appear. Google Scholar

[2] 2.Bonsall, F. F. and Duncan, J., Complete normed algebras, Ergebnesse der Mathematik und ihrer Grenzgebiete, Bd. 80, (Springer-Verlag, 1973). Google Scholar

[3] 3.Douglas, R. G., Banach algebra techniques in operator theory, (Academic Press, 1972). Google Scholar

[4] 4.Dunford, N. and Schwartz, J. T., Linear operators, Part I, (Interscience, 1958). Google Scholar

[5] 5.Glimm, J. and Kadison, R. V., Unitary operators in C*-algebras, Pacific J. Math., 10 (1960), 547–556. Google Scholar

[6] 6.Kadison, R. V. and Ringrose, J. R., Derivations and automorphisms of operator algebras, Comm. Math. Phys., 4 (1967), 32–63. Google Scholar | DOI

[7] 7.Ogasawara, T. and Yoshinaga, K., Weakly completely continuous Banach *-algebras, J. Sci. Hiroshima Univ., Ser. A, 18 (1954), 15–36. Google Scholar

[8] 8.Sakai, S., Weakly compact operators on operator algebras, Pacific J. Math., 14 (1964), 659–664. Google Scholar

[9] 9.Sakai, S., C*-algebras and W*-algebras, Ergebnesse der Mathematik und ihrer Grenzgebiete, Bd. 60, (Springer-Verlag, 1971). Google Scholar

[10] 10.Tomiuk, B. J., Duality and the existence of weakly completely continuous elements in a B*-algebra, Glasgow Math. J., 13 (1972), 56–60. Google Scholar

[11] 11.Vala, K., On compact sets of compact operators, Ann. Acad. Sci. Fenn., Ser. Al, 407 (1967). Google Scholar

Cité par Sources :