Hyperreflexivity of bounded $$N$$ N -cocycle spaces of banach algebras

Samei, Ebrahim; Farsani, Jafar Soltani

doi:10.1007/s00605-014-0628-0

Cited by 9 publications

(20 citation statements)

References 21 publications

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“…If we apply [32,Theorem 5.3], we find that A ♯ has the strong property (B) with a constant given by, M 2 r + (M + 1) 2 . Hence we can use Theorem 4.2 to write δ ♯n (σ(T )) ≤ 2 n−1 (M 2 r + (M + 1) 2 ) n+1 dist r (T, Z n (A, X)).…”

Section: A Bound For the Hyperreflexivity Constantmentioning

confidence: 99%

“…We demonstrated that for a large class of Banach algebras, including nuclear C * -algebras and group algebras of groups with open subgroups of polynomial growth, these sufficient conditions hold, which gave evidence that our conditions are satisfactory. However, our approach in [22] did not give us any information about the hyperreflexivity constant of these spaces.…”

Section: Introductionmentioning

confidence: 97%

“…In the preceding work [22], we considered the extension of the concept of hyperreflexivity to the subspaces of bounded n-linear maps between Banach spaces, taking into account their multilinear structure. We mostly focused on Z n (A, X), the space of bounded n-cocycles from a Banach algebra A into a Banach A-bimodule X, and found sufficient conditions under which Z n (A, X) becomes hyperreflexive.…”

Section: Introductionmentioning

confidence: 99%

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Hyperreflexivity Constants of the Bounded -Cocycle Spaces of Group Algebras and C*-Algebras

Samei

Farsani

2019

J. Aust. Math. Soc.

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We introduce the concept of strong property $(\mathbb{B})$ with a constant for Banach algebras and, by applying a certain analysis on the Fourier algebra of the unit circle, we show that all C*-algebras and group algebras have the strong property $(\mathbb{B})$ with a constant given by $288\unicode[STIX]{x1D70B}(1+\sqrt{2})$. We then use this result to find a concrete upper bound for the hyperreflexivity constant of ${\mathcal{Z}}^{n}(A,X)$, the space of bounded $n$-cocycles from $A$ into $X$, where $A$ is a C*-algebra or the group algebra of a group with an open subgroup of polynomial growth and $X$ is a Banach $A$-bimodule for which ${\mathcal{H}}^{n+1}(A,X)$ is a Banach space. As another application, we show that for a locally compact amenable group $G$ and $1<p<\infty$, the space $CV_{P}(G)$ of convolution operators on $L^{p}(G)$ is hyperreflexive with a constant given by $384\unicode[STIX]{x1D70B}^{2}(1+\sqrt{2})$. This is the generalization of a well-known result of Christensen [‘Extensions of derivations. II’, Math. Scand. 50(1) (1982), 111–122] for $p=2$.

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Section: A Bound For the Hyperreflexivity Constantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hyperreflexivity Constants of the Bounded -Cocycle Spaces of Group Algebras and C*-Algebras

Samei

Farsani

2019

J. Aust. Math. Soc.

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“…More (and not so straightforward) applications can be found in the papers cited. We also remark that the related property B has some somewhat surprising applications to problems of different kinds [3,4,2,6,7,14,16,29,30]. …”

Section: ) -11mentioning

confidence: 98%

Finite dimensional zero product determined algebras are generated by idempotents

Brešar

2016

Expositiones Mathematicae

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An algebra A is said to be zero product determined if every bilinear map f from A × A into an arbitrary vector space X with the property that f (x, y) = 0 whenever x y = 0 is of the form f (x, y) = Φ(x y) for some linear map Φ : A → X . It is known, and easy to see, that an algebra generated by idempotents is zero product determined. The main new result of this partially expository paper states that for finite dimensional (unital) algebras the converse is also true. Thus, if such an algebra is zero product determined, then it is generated by idempotents.

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“…This concept was introduced in [1] and has since turned out to be applicable to a variety of problems; see, for example, [1][2][3]27] and references therein. The main message of [1] is that the class of Banach algebras with property B is quite large, in particular it includes C * -algebras and group algebras of arbitrary locally compact groups.…”

Section: Introductionmentioning

confidence: 99%

Commutators and Square-Zero Elements in Banach Algebras

et al. 2016

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Our initial result states that, in a certain class of Banach algebras which includes C *-algebras and group algebras of locally compact groups, every commutator lies in the closed linear span of square-zero elements. The proof relies on the theory of Banach algebras with property B. We then study several variations and extensions of this result. For instance, we show that in a von Neumann algebra every commutator is actually a finite sum of square-zero elements. We also consider the commutator ideal and the existence of some special square-zero elements.

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Hyperreflexivity of bounded $$N$$ N -cocycle spaces of banach algebras

Cited by 9 publications

References 21 publications

Hyperreflexivity Constants of the Bounded -Cocycle Spaces of Group Algebras and C*-Algebras

Hyperreflexivity Constants of the Bounded -Cocycle Spaces of Group Algebras and C*-Algebras

Finite dimensional zero product determined algebras are generated by idempotents

Commutators and Square-Zero Elements in Banach Algebras

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