Skip to main content Accessibility help
×
Home

Elementary operators on prime C*-algebras II

  • Martin Mathieu (a1)

Extract

Compact elementary operators acting on the algebra ℒ(H) of all bounded operators on some Hilbert space H were characterised by Fong and Sourour in [9]. Akemann and Wright investigated compact and weakly compact derivations on C*-algebras [1], and also studied compactness properties of the sum and the product of the right and the left regular representation of an element in a C*-algebra [2]. They used the concept of a compact Banach algebra element due to Vala [17]: an element a in a Banach algebra A is called compact if the mapping xaxa is compact on A. This notion has been further investigated by Ylinen [18, 19, 20], who showed in particular that a is a compact element of the C*-algebra A if xaxa is weakly compact on A [19].

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Elementary operators on prime C*-algebras II
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Elementary operators on prime C*-algebras II
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Elementary operators on prime C*-algebras II
      Available formats
      ×

Copyright

References

Hide All
1.Akemann, C. A. and Wright, S., Compact and weakly compact derivations of C*-algebras, Pacific J. Math. 85 (1979), 253259.
2.Akemann, C. A. and Wright, S., Compact actions on C*-algebras, Glasgow Math. J. 21 (1980), 143149.
3.Apostol, C. and Fialkow, L. A., Structural properties of elementary operators, Canad. J. Math. 38 (1986), 14851524.
4.Archbold, R. J., On factorial states of operator algebras, J. Functional Analysis 55 (1984), 2538.
5.Barnes, B. A., Murphy, G. J., Smyth, M. R. F. and West, T. T., Riesz and Fredholm theory in Banach algebras, Pitman Research Notes in Mathematics 67 (1982).
6.Breuer, M., Fredholm theories in von Neumann algebras I, Math. Ann. 178 (1968), 243254.
7.Dixmier, J., Les C*-algébres et leurs représentations, (Gauthier-Villars, 1969).
8.Dunford, N. and Schwartz, J. T., Linear operators Part I, (Interscience, New York, 1958).
9.Fong, C. K. and Sourour, A. R., On the operator identity σAkXBk = 0, Canad. J. Math. 31 (1979), 845857.
10.Ho, Y., A note on derivations, Bull. Inst. Math. Acad. Sinica 5 (1977), 15.
11.Magajna, B., A system of operator equations, Canad. Math. Bull. 30 (1987), 200209.
12.Martindale, W. S., Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576584.
13.Mathieu, M., Elementary operators on prime C*-algebras, I, to appear.
14.Mathieu, M., Applications of ultraprime Banach algebras in the theory of elementary operators, Thesis, (Tübingen, 1986).
15.Pedersen, G. K., C*-atgebras and their automorphism groups, (Academic Press, 1979).
16.Vala, K., On compact sets of compact operators, Ann. Acad. Sci. Fenn. Ser. A I 351 (1964).
17.Vala, K., Sur les éléments compacts d'une algèbre normée, Ann. Acad. Sci. Fenn. Ser. A I 407 (1967).
18.Ylinen, K., Compact and finite-dimensional elements of normed algebras, Ann. Acad. Sci. Fenn. Ser. A I 428 (1968).
19.Ylinen, K., Dual C*-algebras, weakly semi-completely continuous elements, and the extreme rays of the positive cone, Ann. Acad. Sci. Fenn. Ser. A 1 599 (1975).
20.Ylinen, K., Weakly completely continuous elements of C*-algebras, Proc. Amer. Math. Soc. 52 (1975), 323326.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed