Affiliation:
1. Department of Mathematics , Aligarh Muslim University , Aligarh - India
Abstract
Abstract
Let χ be a Banach space of dimension n > 1 and 𝔘 ⊂ 𝔅(χ) be a standard operator algebra. In the present paper it is shown that if a mapping d : 𝔘 → 𝔘 (not necessarily linear) satisfies
d
(
[
[
U
,
V
]
,
W
]
)
=
[
[
d
(
U
)
,
V
]
,
W
]
+
[
[
U
,
d
(
V
)
,
W
]
]
+
[
[
U
,
V
]
,
d
(
W
)
]
d\left( {\left[ {\left[ {U,V} \right],W} \right]} \right) = \left[ {\left[ {d\left( U \right),V} \right],W} \right] + \left[ {\left[ {U,d\left( V \right),W} \right]} \right] + \left[ {\left[ {U,V} \right],d\left( W \right)} \right]
for all U, V, W ∈ 𝔘, then d =ψ + τ, where ψ is an additive derivation of 𝔘 and τ : 𝔘 → 𝔽I vanishes at second commutator [[U, V ], W ] for all U, V, W ∈ 𝔘. Moreover, if d is linear and satisfies the above relation, then there exists an operator S ∈ 𝔘 and a linear mapping τ from 𝔘 into 𝔽I satisfying τ ([[U, V ], W ]) = 0 for all U, V, W ∈ 𝔘, such that d(U) = SU − US + τ (U) for all U ∈ 𝔘.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献