Common fixed point properties and amenability of a class of Banach algebras

Desaulniers, Shawn; Nasr-Isfahani, Rasoul; Nemati, Mehdi

doi:10.1016/j.jmaa.2012.12.057

Cited by 13 publications

(7 citation statements)

References 18 publications

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“…Remark 4.9. A common fixed point property for affine actions of P 1 (A) with a weak topology on compact convex sets has been studied in [11] for left amenable F-algebras A.…”

Section: Fixed Point Properties For F-algebrasmentioning

confidence: 99%

Algebraic and analytic properties of semigroups related to fixed point properties of non-expansive mappings

Lau

Zhang

2019

Semigroup Forum

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The purpose of this paper is to give an updated survey on various algebraic and analytic properties of semigroups related to fixed point properties of semigroup actions on a non-empty closed convex subset of a Banach space or, more generally, a locally convex topological vector space. Dedicated to Professor Karl H. Hofmann with admiration and respect1991 Mathematics Subject Classification. Primary 43A07 Secondary 43A60, 22D05 46B20.

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“…Remark 4.9. A common fixed point property for affine actions of P 1 (A) with a weak topology on compact convex sets has been studied in [11] for left amenable F-algebras A.…”

Section: Fixed Point Properties For F-algebrasmentioning

confidence: 99%

Algebraic and analytic properties of semigroups related to fixed point properties of non-expansive mappings

Lau

Zhang

2019

Semigroup Forum

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“…In conclusion of this section, let us mention that Lau products of Banach algebras was first introduced and studied by Lau [12] for a large class of Banach algebras known as Lau algebras; recall that a Lau algebra L is a Banach algebra which is the predual of a von Neumann algebra m for which the identity of m is multiplicative on L; see also [4] and [14]. The subject of this large class of Banach algebras originated with a paper published in 1983 by Lau [12] in which he referred to them as "F-algebras".…”

Section: Preliminariesmentioning

confidence: 99%

Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras

Ghaderi

Nasr-Isfahani

Nemati

2016

Mathematica Slovaca

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Let A and B be two Banach algebras and let θ be a nonzero character on B. In this paper, we deal with the θ-Lau product A × θ B that was first introduced by A. T. Lau for certain Banach algebras known as Lau algebras and recently by M. S. Monfared for all Banach algebras; we study pseudo-amenability, pseudo-contractibility and character pseudo-amenability of A × θ B and their relations with A and B.

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“…Example 2.12. (1). Let H be a locally compact hypergroup with the convolution product * , defined on M(H), the space of bounded Radon measures on H. Concerning the general theory of hypergroups we refer the reader to [2].…”

Section: φ-Ergodic Propertymentioning

confidence: 99%

“…Recall that a Lau algebra A is a Banach algebra which is the predual of von Neumann algebra M such that the identity element e of M is a multiplicative linear functional on A. In this case, the e-means of norm one are nothing but the topological left invariant means on A * ; see [7] and [8], [1] for more details concerning the left amenability of Lau algebras. Following [7], A is called left amenable if there is a topological left invariant mean on A * .…”

Section: Corollary 215 Let a Be A Banach Algebra With φ ∈ ∆(A) Then A Is φ-Amenable With A φ-Mean Of Norm One If And Only If Any Banach Rmentioning

confidence: 99%

On $\phi$-ergodic property of Banach modules

Nemati¹

2015

Bull. Belg. Math. Soc. Simon Stevin

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Let A be a Banach algebra and let φ be a non-zero character on A. We introduce the notion of φ-ergodic property for a Banach right A-module X. This concept considerably generalizes the existence of φ-means of norm one on A * . We also show that the φ-ergodic property of X is related to some other properties such as a Hahn-Banach type extension property and the existence of φ-means of norm one on a certain subspace of A * . Finally, we give some characterizations for φ-amenability of a Banach algebra in terms of its closed ideals.

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Common fixed point properties and amenability of a class of Banach algebras

Cited by 13 publications

References 18 publications

Algebraic and analytic properties of semigroups related to fixed point properties of non-expansive mappings

Algebraic and analytic properties of semigroups related to fixed point properties of non-expansive mappings

Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras

On $\phi$-ergodic property of Banach modules

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