Local derivations of reflexive algebras II

Wu, Jing

doi:10.1090/S0002-9939-01-05792-6

Local derivations of reflexive algebras II
HTML articles powered by AMS MathViewer

by Jing Wu

Proc. Amer. Math. Soc. 129 (2001), 1733-1737

DOI: https://doi.org/10.1090/S0002-9939-01-05792-6

Published electronically: January 17, 2001

PDF | Request permission

Abstract:

Let ${\mathcal A}$ be a reflexive algebra in Banach space $X$ such that both $0_+\not = 0$ and $X_-\not = X$ in Lat$\mathcal A$. Then every local derivation of $\mathcal A$ into itself is a derivation.

References

MR 0718951

De Guang Han and Shu Yun Wei, Local derivations of nest algebras, Proc. Amer. Math. Soc. 123 (1995), no. 10, 3095–3100. MR 1246521, DOI 10.1090/S0002-9939-1995-1246521-1
Wu Jing, Local derivations of reflexive algebras, Proc. Amer. Math. Soc. 125 (1997), no. 3, 869–873. MR 1363440, DOI 10.1090/S0002-9939-97-03720-9
Richard V. Kadison, Local derivations, J. Algebra 130 (1990), no. 2, 494–509. MR 1051316, DOI 10.1016/0021-8693(90)90095-6
David R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), no. 2, 283–299. MR 935008, DOI 10.2307/2374503
David R. Larson and Ahmed R. Sourour, Local derivations and local automorphisms of ${\scr B}(X)$, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 187–194. MR 1077437, DOI 10.1090/pspum/051.2/1077437
W. E. Longstaff, Strongly reflexive lattices, J. London Math. Soc. (2) 11 (1975), no. 4, 491–498. MR 394233, DOI 10.1112/jlms/s2-11.4.491
Lawrence M. Graves, The Weierstrass condition for multiple integral variation problems, Duke Math. J. 5 (1939), 656–660. MR 99