When is the Range of a Multiplier on a Banach Algebra Closed?

Ülger, A.

doi:10.1007/s00209-006-0003-5

Cited by 4 publications

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References 17 publications

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“…We recall that every maximal ideal Ker(γ ) of L 1 (G) has a bounded approximate identity. A justification (valid for all the Banach algebras considered in this paper) of this affirmation can be found in [47,Lemma 4.3]. We also recall that, for any γ ∈ G considered as a multiplicative functional on L 1 (G) and for m and n in L 1 (G) * * , we have γ, mn = γ, m .…”

Section: Applications To the Study Of Sets Of Spectral Synthesismentioning

confidence: 81%

An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

Ülger

2010

Journal of Functional Analysis

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Let E be a compact perfect subset of the real line R such that the restriction of the Fourier transform a → a| E from L 1 (R) into C(E) is onto. Helson proved that then, for μ ∈ M(E), lim |y|→∞ | μ(y)| = 0 is possible only if μ = 0. In this paper we present an abstract version of this theorem of Helson and provide some applications of it to the study of sets of spectral synthesis and sets of uniqueness.

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Section: Applications To the Study Of Sets Of Spectral Synthesismentioning

confidence: 81%

An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

Ülger

2010

Journal of Functional Analysis

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“…Let A be a Banach algebra with a bounded approximate identity such that every proper closed ideal of A is contained in a proper closed ideal with a bounded approximate identity. From Theorem 4.7 of [18] and Theorem 2.4 we have the following result.…”

Section: Corollary 23mentioning

confidence: 89%

The Acceptance of Mobile Health Services by Physicians: The Case of Iran

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On the structure of ideals and multipliers: A unified approach

Мbekhta

Neufang

2019

Proc. Amer. Math. Soc.

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We study the structure of one-sided ideals in a Banach algebra A \mathcal {A} . We find very general conditions under which any left (right) ideal is of the form A q \mathcal {A} q ( q A q \mathcal {A} ) for some idempotent right (left) multiplier on A \mathcal {A} . We further show that a large class of one-sided multipliers can be realized as a product of an invertible and an idempotent multiplier. Applying our results to algebras over locally compact quantum groups and C ∗ C^* -algebras, we demonstrate that our approach generalizes and unifies various theorems from abstract harmonic analysis and operator algebra theory. In particular, we generalize results of Bekka (and Reiter), Berglund, Forrest, and Lau–Losert. We also deduce the Choquet–Deny theorem for compact groups as an application of our approach. Moreover, we answer, for a certain class of measures on a compact group, a question of Ülger which, in the abelian case, goes back to Beurling (1938).

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When is the Range of a Multiplier on a Banach Algebra Closed?

Cited by 4 publications

References 17 publications

An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

The Acceptance of Mobile Health Services by Physicians: The Case of Iran

On the structure of ideals and multipliers: A unified approach

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