Additive mappings derivable at non-trivial idempotents on Banach algebras

References

• Alaminos , J , Brešar , M , Extremera , J and Villena , AR . 2007 . Characterizing homomorphisms and derivations on C*-algebras . Proc. Roy. Soc. Edinburgh. Sect. A. , 137 : 1 – 7 .
   Google Scholar
• An , R and Hou , J . 2009 . Characterizations of derivations on triangular rings: additive maps derivable at idempotents . Linear Algebra Appl. , 431 : 1070 – 1080 .
   Web of Science ®Google Scholar
• Brešar , M . 1988 . Jordan derivation on semiprime rings . Proc. Amer. Math. Soc. , 104 : 1003 – 1006 .
   Web of Science ®Google Scholar
• Brešar , M . 2007 . Characterizing homomorphisms, multipliers and derivations in rings with idempotents . Proc. Roy. Soc. Edinburgh. Sect. A. , 137 : 9 – 21 .
   Google Scholar
• Chebotar , MA , Ke , W-F and Lee , P-H . 2004 . Maps characterized by action on zero products . Pacific. J. Math. , 216 : 217 – 228 .
   Web of Science ®Google Scholar
• Chernoff , PR . 1973 . Representations, automorphisms, and derivations of some operator algebras . J. Funct. Anal. , 12 : 275 – 289 .
   Google Scholar
• Cheung , W-S . 2001 . Commuting maps of triangular algebras . J. London Math. Soc. , 63 : 117 – 127 .
   Web of Science ®Google Scholar
• Christensen , E . 1977 . Derivations of nest algebras . Math. Ann. , 229 : 155 – 161 .
   Web of Science ®Google Scholar
• Crist , RL . 1996 . Local derivations on operator algebras . J. Funct. Anal. , 135 : 76 – 92 .
   Web of Science ®Google Scholar
• Dales , HG . 2000 . “ Banach Algebras and Automatic Continuity ” . In London Mathematical Society Monographs , Oxford : Oxford University Press .
   Google Scholar
• Davision , KR . 1988 . “ Nest Algebras ” . In Pitman Research Notes in Mathematics Series , Vol. 191 , Essex , , UK : Longman Scientific and Technical, Harlow .
   Google Scholar
• Gilfeather , F and Larson , AR . 1982 . Nest subalgebras of von Neumann algebras . Adv. Math. , 46 : 171 – 199 .
   Web of Science ®Google Scholar
• Han , DG . 1993 . Additive derivations of nest algebras . Proc. Amer. Math. Soc. , 119 : 1165 – 1169 .
   Web of Science ®Google Scholar
• Han , DG . 1996 . Continuity and linearity of additive derivations of nest algebras on Banach spaces . Chinese Ann. Math. Ser. B , 17 : 227 – 236 .
   Web of Science ®Google Scholar
• Hou , J and An , R . 2011 . Additive maps on rings behaving like derivations at idempotent-product elements . J. Pure Appl. Algebra, , 215 : 1852 – 1862 .
   Web of Science ®Google Scholar
• Hou , CJ and Han , DG . 1998 . Derivations and isomorphisms of certain reflexive operator algebras . Acta Math. Sinica (in Chinese) , 14 : 105 – 112 .
   Web of Science ®Google Scholar
• Hou , CJ and Qi , X . 2008 . Additive maps derivable at some points on 𝒥-subspace lattice algebras . Linear Algebra Appl. , 429 : 1851 – 1863 .
   Web of Science ®Google Scholar
• Jiao , M and Hou , J . 2010 . Additive maps derivable or Jordan derivable at zero point on nest algebras . Linear Algebra Appl. , 432 : 2984 – 2994 .
   Web of Science ®Google Scholar
• Jing , W , Lu , S and Li , P . 2002 . Characterization of derivation on some operator algebras . Bull. Austr. Math. Soc. , 66 : 227 – 232 .
   Web of Science ®Google Scholar
• Johnson , BE . 1996 . Symmetric amenability and nonexistence of Lie and Jordan derivations . Math. Proc. Camb. Phil. Soc. , 120 : 455 – 473 .
   Web of Science ®Google Scholar
• Johnson , BE . 2001 . Local derivations on C*-algebras are derivations . Trans. Amer. Math. Soc. , 353 : 313 – 325 .
   Web of Science ®Google Scholar
• Johnson , BE and Sinclair , AM . 1968 . Continuity of derivations and a problem of Kaplansky . Amer. J. Math. , 39 : 1067 – 1073 .
   Web of Science ®Google Scholar
• Kadison , RV , Lance , EC and Ringrose , JR . 1967 . Derivations and automorphisms of operator algebras II . J. Funct. Anal. , 1 : 204 – 221 .
   Google Scholar
• Kadison , RV and Ringrose , JR . 1967 . Derivations and automorphisms of operator algebras . Comm. Math. Phys. , 4 : 32 – 63 .
   Google Scholar
• Knowles , GJ . 1987 . Quotients of nest algebras with trivial commutator . Pacific J. Math. , 127 : 121 – 126 .
   Web of Science ®Google Scholar
• Li , J , Pan , Z and Xu , H . 2007 . Characterizations of isomorphisms and derivations of some algebras . J. Math. Anal. Appl. , 332 : 1314 – 1322 .
   Web of Science ®Google Scholar
• Li , J and Pendharkar , H . 2000 . Derivations of certain operator algebras . Intern. J. Math. Math. Sci. , 24 : 345 – 349 .
   Google Scholar
• Li , J and Zhou , J . 2011 . Characterizations of Jordan derivations and Jordan homomorphisms . Linear Multilinear Algebra , 59 : 193 – 204 .
   Web of Science ®Google Scholar
• Lu , F . 2009 . Characterizations of derivations and Jordan derivations on Banach algebras . Linear Algebra Appl. , 430 : 2233 – 2239 .
   Web of Science ®Google Scholar
• Pedersen , GK . 1979 . “ C*-algebras and their automorphism groups ” . In London Mathematical Society Monographs, First Series , Vol. 14 , London : Academic Press .
   Google Scholar
• Pop , F . 1990 . Derivations of certain nest-subalgebras of von Neumann algebras . Oper. Theory Adv. Appl, , 43 : 279 – 288 .
   Google Scholar
• Qi , X and Hou , J . 2010 . Characterizations of derivations of Banach space nest algebras: All-derivable points . Linear Algebra Appl. , 432 : 3183 – 3200 .
   Web of Science ®Google Scholar
• Ringrose , JR . 1965 . On some algebras of operators . Proc. London Math. Soc. , 15 : 61 – 83 .
   Web of Science ®Google Scholar
• Spivac , M . 1985 . Derivations of nest algebras on Banach spaces . Israel J. Math. , 50 : 193 – 200 .
   Web of Science ®Google Scholar
• Zhang , J and Yu , W . 2006 . Jordan derivations of triangular algebras . Linear Algebra Appl. , 419 : 251 – 255 .
   Web of Science ®Google Scholar
• Zhu , J . 1995 . Local derivation of nest algebras . Proc. Amer. Math. Soc. , 123 : 739 – 742 .
   Web of Science ®Google Scholar
• Zhu , J . 2007 . All-derivable points of operator algebras . Linear Algebra Appl. , 427 : 1 – 5 .
   Web of Science ®Google Scholar
• Zhu , J and Xiong , C . 2007 . Derivable mappings at unit operator on nest algebras . Linear Algebra Appl. , 422 : 721 – 735 .
   Web of Science ®Google Scholar
• Zhu , J and Xiong , C . 2008 . All-derivable points in continuous nest algebras . J. Math. Anal. Appl. , 340 : 843 – 853 .
   Web of Science ®Google Scholar