The Bochner-Schoenberg-Eberlein Property for $L^{1}(\mathbb{R}^{+})$

Kamali, Zeinab; Bami, M. Lashkarizadeh

doi:10.1007/s00041-013-9303-4

Cited by 10 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(iii) Suppose that σ A ∈ c BSE A ϕ and σ X ∈ c BSE X ϕ . For any ϕ ∈ ∆(A), define π A ϕ (a) =â(ϕ) and π X ϕ (x) =x(ϕ) for all a ∈ A and x ∈ X, and define π ϕ (a, x) = 8 N. Alizadeh, A. Ebadian, S. Ostadbashi and A. Jabbari [8] (π A ϕ (a), π X ϕ (x)) for all (a, x) ∈ A ⊕ 1 X. Let ϕ 1 , .…”

Section: Bse Module Property Onmentioning

confidence: 99%

See 1 more Smart Citation

The Bochner–schoenberg-Eberlein Property of Extensions of Banach Algebras and Banach Modules

Alizadeh¹,

Ebadian

Ostadbashi³

et al. 2021

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

Let A be a Banach algebra and let X be a Banach A-bimodule. We consider the Banach algebra ${A\oplus _1 X}$ , where A is a commutative Banach algebra. We investigate the Bochner–Schoenberg–Eberlein (BSE) property and the BSE module property on $A\oplus _1 X$ . We show that the module extension Banach algebra $A\oplus _1 X$ is a BSE Banach algebra if and only if A is a BSE Banach algebra and $X=\{0\}$ . Furthermore, we consider $A\oplus _1 X$ as a Banach $A\oplus _1 X$ -module and characterise the BSE module property on $A\oplus _1 X$ . We show that $A\oplus _1 X$ is a BSE Banach $A\oplus _1 X$ -module if and only if A and X are BSE Banach A-modules.

show abstract

Section: Bse Module Property Onmentioning

confidence: 99%

“…This notion was introduced by Takahasi and Hatori in [16] and it is characterised by Kaniuth and Ülger in [11]. Classes of Banach algebras that are BSE Banach algebras and are not BSE Banach algebras have been investigated in [1,5,7,8,9,10]. Takahasi, in [15], generalised the BSE-property to Banach modules.…”

Section: Introductionmentioning

confidence: 99%

The Bochner–schoenberg-Eberlein Property of Extensions of Banach Algebras and Banach Modules

Alizadeh¹,

Ebadian

Ostadbashi³

et al. 2021

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…The theory of BSE-algebras for the first time introduced and investigated by Takahasi and Hatori; see [11] and two other notable works [5,3]. In [3], the authors answered to a question raised in [11].…”

Section: Introductionmentioning

confidence: 99%

On character space of the algebra of BSE-functions

Fozouni

2017

Preprint

View full text Add to dashboard Cite

Suppose that A is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra CBSE(∆(A)) consisting of all BSEfunctions on ∆(A) where ∆(A) denotes the character space of A. Indeed, in the case that A = C0(X) where X is a non-empty locally compact Hausdroff space, we give a complete characterization of ∆(CBSE(∆(A))) and in the general case we give a partial answer.Also, using the Fourier algebra, we show that CBSE(∆(A)) is not a C * -algebra in general. Finally for some subsets E of A * , we define the subspace of BSE-like functions on ∆(A) ∪ E and give a nice application of this space related to Goldstine's theorem.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The theory of BSE-algebras was first introduced and investigated by Takahasi and Hatori; see [20] and two other notable works [15,13]. In [13], the authors answered a question raised in [20]. Examples of BSE-algebras are the group algebra L 1 (G) of a locally compact abelian group G, the Fourier algebra A(G) of a locally compact amenable group G, all commutative C * -algebras, the disk algebra, and the Hardy algebra on the open unit disk.…”

Section: Introductionmentioning

confidence: 99%

BSE-Property for Some Certain Segal and Banach Algebras

Fozouni

Nemati

2019

Mediterr. J. Math.

View full text Add to dashboard Cite

For a commutative semi-simple Banach algebra A which is an ideal in its second dual we give a necessary and sufficient condition for an essential abstract Segal algebra in A to be a BSE-algebra. We show that a large class of abstract Segal algebras in the Fourier algebra A(G) of a locally compact group G are BSE-algebra if and only if they have bounded weak approximate identities. Also, in the case that G is discrete we show that A cb (G) is a BSE-algebra if and only if G is weakly amenable. We study the BSE-property of some certain Segal algebras implemented by local functions that were recently introduced by J. Inoue and S.-E. Takahasi. Finally we give a similar construction for the group algebra implemented by a measurable and sub-multiplicative function. Recently, J. Inoue and S.-E. Takahasi in [11] investigated abstract Segal algebras in a non-unital commutative semi-simple regular Banach algebra A such that A has a bounded approximate identity in A c where A c = {a ∈ A : a has compact support},

show abstract

The Bochner-Schoenberg-Eberlein Property for $L^{1}(\mathbb{R}^{+})$

Cited by 10 publications

References 9 publications

The Bochner–schoenberg-Eberlein Property of Extensions of Banach Algebras and Banach Modules

The Bochner–schoenberg-Eberlein Property of Extensions of Banach Algebras and Banach Modules

On character space of the algebra of BSE-functions

BSE-Property for Some Certain Segal and Banach Algebras

Contact Info

Product

Resources

About