Continuity of derivations on some semiprime Banach algebra

Garimella, Ramesh V.

doi:10.1090/s0002-9939-1987-0870787-6

Cited by 10 publications

(4 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence sx £ CC=X Jn ■ Since fl^li Jn = {0}, it follows that sx = 0. is a closed ideal, RnS(D) is a nilpotent ideal (see [6]). Hence by Lemma 2.1 of [5], S(D) is a nilpotent ideal. This is false.…”

Section: Preliminariesmentioning

confidence: 91%

See 1 more Smart Citation

On nilpotency of the separating ideal of a derivation

Garimella¹

1993

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

Abstract. We prove that the separating ideal S(D) of any derivation D on a commutative unital algebra B is nilpotent if and only if S(D) n (f) R") is a nil ideal, where R is the Jacobson radical of B . Also we show that any derivation D on a commutative unital semiprime Banach algebra B is continuous if and only if f)(S(D))" = {0} . Further we show that the set of all nilpotent elements of S(D) is equal to (~){S(D)nP), where the intersection runs over all nonclosed prime ideals of B not containing S{D). As a consequence, we show that if a commutative unital Banach algebra has only countably many nonclosed prime ideals then the separating ideal of a derivation is nilpotent.

show abstract

Section: Preliminariesmentioning

confidence: 91%

“…Proof. For the equivalence of (ii) and (iii) refer to Theorem 3.1 of [5]. Obviously (i) implies (ii).…”

Section: Preliminariesmentioning

confidence: 99%

On nilpotency of the separating ideal of a derivation

Garimella¹

1993

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This thoery has been an active field of research during the last fifty years. The automatic continuity of the derivations on different structures in mathematics has attracted the attention of the researchers and, specifically, has been mainly developed in the context of Banach algebras and studied extensively (see for example, [8], [17], [18], [20], [22], [28]). The continuity of derivations from a Banach algebra into a Banach bimodule arises in a number of situations.…”

Section: Introductionmentioning

confidence: 99%

Automatic continuity of Some linear mappings from certain products of Banach algebras

Farhadi¹,

Ghaderi²,

Ghahramani³

2019

Preprint

View full text Add to dashboard Cite

Let A and U be Banach algebras and θ be a nonzero character on A. Then the Lau product Banach algebra A × θ U associated with the Banach algebras A and U is the l 1 -direct sum A ⊕ U equipped with the algebra multiplication (a, u)(a ′ , u ′ ) = (ab, θ(a)u ′ + θ(a ′ )u + uu ′ ) (a, a ′ ∈ A, u, u ′ ∈ U ) and l 1 -norm. In this paper we shall investigate the derivations and multipliers from this Banach algebras and study the automatic continuity of these mappings. We also study continuity of the derivations for some special cases of Banach algebra U and Banach A × θ U -bimodule X and establish various results on the continuity of derivations and give some examples.

show abstract

“…In particular, RV Garmilla that is interested in (Q'1) (see [3], [4], [5]) and V. Runde has given in [10] some results on these two issues.…”

Section: Introductionmentioning

confidence: 99%