A clarified study on the G-complete symmetry Banach algebra is given. A Wiener type Banach algebra as well as its stucture is introduced and studied. An application of this algebra is presented.
Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3...Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3 for all A, B C .4, where [A, B]3 is the 3-commutator of A, B defined by [A, B]3 = [[[A, B], B], B] with [A, B] = AB - BA. The main result in this paper is shown that, if Ф is a surjective map on A, then Ф is strong 3-commutativity preserving if and only if there exist a functional h ： A→F and a scalar λ∈F with λ^4 = 1 such that Ф（A） = λA ＋ h（A）I for all A ∈A.展开更多
The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then the...The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then there exists an element a in the socle of A such that [d, d′] is the inner derivation implemented bv a.展开更多
基金This work wassupported by the National Natural Science Foundation of China (Grant Nos. 19631070 & 10171019), Natural Science Foundation of Hunan Province, China (Grant No. OOTJJY2001) and National Science Foundation of Zhejiang Province, China (Grant N
文摘A clarified study on the G-complete symmetry Banach algebra is given. A Wiener type Banach algebra as well as its stucture is introduced and studied. An application of this algebra is presented.
基金Supported by Natural Science Foundation of China(Grant No.11671294)
文摘Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B（X）. A map Ф ： A→A is said to be strong 3-commutativity preserving if [Ф（A）, Ф（B）]a = [A, B]3 for all A, B C .4, where [A, B]3 is the 3-commutator of A, B defined by [A, B]3 = [[[A, B], B], B] with [A, B] = AB - BA. The main result in this paper is shown that, if Ф is a surjective map on A, then Ф is strong 3-commutativity preserving if and only if there exist a functional h ： A→F and a scalar λ∈F with λ^4 = 1 such that Ф（A） = λA ＋ h（A）I for all A ∈A.
文摘The purpose of this paper is to study derivations d, d′ defined on a Banach algebra A such that the spectrum a（[dx, d′x]） is finite for all x ∈ A. In particular we show that if the algebra is semisimple, then there exists an element a in the socle of A such that [d, d′] is the inner derivation implemented bv a.
