Derivations implemented by local multipliers
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Abstract:
A condition on a derivation of an arbitrary C*-algebra is presented entailing that it is implemented as an inner derivation by a local multiplier.References
- Pere Ara, On the symmetric algebra of quotients of a $C^*$-algebra, Glasgow Math. J. 32 (1990), no. 3, 377–379. MR 1073678, DOI 10.1017/S0017089500009460
- Pere Ara and Martin Mathieu, A local version of the Dauns-Hofmann theorem, Math. Z. 208 (1991), no. 3, 349–353. MR 1134580, DOI 10.1007/BF02571531
- Pere Ara and Martin Mathieu, An application of local multipliers to centralizing mappings of $C^*$-algebras, Quart. J. Math. Oxford Ser. (2) 44 (1993), no. 174, 129–138. MR 1222369, DOI 10.1093/qmath/44.2.129
- George A. Elliott, Automorphisms determined by multipliers on ideals of a $C^*$-algebra, J. Functional Analysis 23 (1976), no. 1, 1–10. MR 0440372, DOI 10.1016/0022-1236(76)90054-9
- I. N. Herstein, A condition that a derivation be inner, Rend. Circ. Mat. Palermo (2) 37 (1988), no. 1, 5–7. MR 994134, DOI 10.1007/BF02844264
- Richard V. Kadison, Derivations of operator algebras, Ann. of Math. (2) 83 (1966), 280–293. MR 193527, DOI 10.2307/1970433
- V. K. Kharchenko, Automorphisms and derivations of associative rings, Mathematics and its Applications (Soviet Series), vol. 69, Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the Russian by L. Yuzina. MR 1174740, DOI 10.1007/978-94-011-3604-4
- Martin Mathieu, Elementary operators on prime $C^*$-algebras. I, Math. Ann. 284 (1989), no. 2, 223–244. MR 1000108, DOI 10.1007/BF01442873
- Martin Mathieu, The $cb$-norm of a derivation, Algebraic methods in operator theory, Birkhäuser Boston, Boston, MA, 1994, pp. 144–152. MR 1284942
- Dorte Olesen, Derivations of $AW^{\ast }$-algebras are inner, Pacific J. Math. 53 (1974), 555–561. MR 358378, DOI 10.2140/pjm.1974.53.555
- Gert K. Pedersen, Approximating derivations on ideals of $C^*$-algebras, Invent. Math. 45 (1978), no. 3, 299–305. MR 477792, DOI 10.1007/BF01403172
- Shôichirô Sakai, Derivations of $W^{\ast }$-algebras, Ann. of Math. (2) 83 (1966), 273–279. MR 193528, DOI 10.2307/1970432
- Shôichirô Sakai, Derivations of simple $C^{\ast }$-algebras. II, Bull. Soc. Math. France 99 (1971), 259–263. MR 293414, DOI 10.24033/bsmf.1719
- D. W. B. Somerset, The proximinality of the centre of a $C^*$-algebra, J. Approx. Theory 89 (1997),114–117.
Additional Information
- Martin Mathieu
- Affiliation: The Fields Institute for Research in Mathematical Sciences, Waterloo, Ontario, Canada
- Address at time of publication: Department of Mathematics, St. Patrick’s College, Maynooth, Co. Kildare, Ireland
- MR Author ID: 201466
- Email: mm@maths.may.ie
- Received by editor(s): September 23, 1996
- Additional Notes: This work was done while the author was a Visiting Fellow at The Fields Institute for Research in Mathematical Sciences, Waterloo, Ontario, Canada, supported by the Deutsche Forschungsgemeinschaft (DFG), to both of which he is very grateful
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1133-1138
- MSC (1991): Primary 46L57; Secondary 47B47, 16N60
- DOI: https://doi.org/10.1090/S0002-9939-98-04394-9
- MathSciNet review: 1452813