zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Additive Lie ($\xi $-Lie) derivations and generalized Lie ($\xi $-Lie) derivations on nest algebras. (English) Zbl 1207.47081
Summary: For a scalar $\xi $, a notion of (generalized) $\xi $-Lie derivations is introduced which coincides with the notion of (generalized) Lie derivations if $\xi =1$. Some characterizations of additive (generalized) $\xi $-Lie derivations on the triangular algebras and the standard operator subalgebras of Banach space nest algebras are given. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) $\xi $-Lie derivation with $\xi \neq 1$ if and only if it is an additive (generalized) derivation satisfying $L(\xi A)=\xi L(A)$ for all $A$.

MSC:
47L35Nest algebras, CSL algebras
16W25Derivations, actions of Lie algebras (associative rings and algebras)
WorldCat.org
Full Text: DOI arXiv
References:
[1] Brešar, M.: On the distance of the composition of two derivations to the generalized derivations, Glasgow math. J. 33, 89-93 (1991) · Zbl 0731.47037 · doi:10.1017/S0017089500008077
[2] Brešar, M.: Commuting traces of biadditive mappings commutativity-preserving mappings and Lie mappings, Trans. amer. Math. soc. 335, 525-546 (1993) · Zbl 0791.16028 · doi:10.2307/2154392
[3] Brešar, M.: Jordan derivations revisited, Math. proc. Cambridge philos. Soc. 139, 411-425 (2005) · Zbl 1092.16020 · doi:10.1017/S0305004105008601
[4] Brooke, J. A.; Busch, P.; Pearson, B.: Commutativity up to a factor of bounded operators in complex Hilbert spaces, Roy. soc. Lond. proc. Ser. A math phys. Eng. sci. A 458, No. 2017, 109-118 (2002) · Zbl 1037.81009 · doi:10.1098/rspa.2001.0858
[5] Cheung, W. S.: Commuting maps of triangular algebras, J. London math soc. 63, 117-127 (2001) · Zbl 1014.16035 · doi:10.1112/S0024610700001642
[6] Cheung, W. S.: Lie derivations of triangular algebras, Linear multilinear algebra 51, 299-310 (2003) · Zbl 1060.16033 · doi:10.1080/0308108031000096993
[7] Christensen, E.: Derivations of nest algebras, Math. ann. 229, 155-161 (1977) · Zbl 0356.46057 · doi:10.1007/BF01351601
[8] Davidson, K. R.: Nest algebras, Pitman research notes in mathematics 191 (1988)
[9] Han, D. G.: Additive derivations of nest algebras, Proc. amer. Math. soc. 119, 1165-1169 (1993) · Zbl 0810.47040 · doi:10.2307/2159979
[10] Han, D. G.: Continuity and linearity of additive derivations of nest algebras on Banach spaces, Chinese ann. Math. ser. B 17, 227-236 (1996) · Zbl 0856.47028
[11] Hou, C. J.; Han, D. G.: Derivations and isomorphisms of certain reflexive operator algebras, Acta math. Sinica 14, 105-112 (1998) · Zbl 0914.47043 · doi:10.1007/BF02563890
[12] Hou, J. C.; Qi, X. F.: Generalized Jordan derivation on nest algebras, Linear algebra appl. 430, 1479-1485 (2009) · Zbl 1155.47059 · doi:10.1016/j.laa.2007.10.020
[13] Hvala, B.: Generalized Lie derivations in prime rings, Taiwanese J. Math. 11, 1425-1430 (2007) · Zbl 1143.16035
[14] Johnson, B. E.: Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. proc. Cambridge philos. Soc. 120, 455-473 (1996) · Zbl 0888.46024 · doi:10.1017/S0305004100075010
[15] Kassel, C.: Quantum groups, (1995) · Zbl 0808.17003
[16] Mathieu, M.; Villena, A. R.: The structure of Lie derivations on C$\ast $-algebras, J. funct. Anal. 202, 504-525 (2003) · Zbl 1032.46086 · doi:10.1016/S0022-1236(03)00077-6
[17] Šemrl, P.: Additive derivations of some operator algebras, Illinois J. Math. 35, 234-240 (1991) · Zbl 0705.46035
[18] X.F. Qi, J.C. Hou, Characterizations of \xi -Lie multiplicative isomorphisms, preprint.
[19] Spivac, M.: Derivations of nest algebras on Banach spaces, Israel J. Math. 50, No. 2, 193-200 (1985)
[20] Zhang, J. H.: Lie derivations on nest subalgebras of von Neumann algebras, Acta math. Sinica 46, 657-664 (2003) · Zbl 1054.47061
[21] Zhang, J. H.; Yu, W. Y.: Jordan derivations of triangular algebras, Linear algebra appl. 419, 251-255 (2006) · Zbl 1103.47026 · doi:10.1016/j.laa.2006.04.015