Displaying similar documents to “Pseudo-amenability of Brandt semigroup algebras”

Counter examples for pseudo-amenability of some semigroup algebras

Amir Sahami (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this short note, we give some counter examples which show that [11, Proposition 3.5] is not true. As a consequence, the arguments in [11, Proposition 4.10] is not valid.

Approximate amenability of semigroup algebras and Segal algebras

H. G. Dales, R. J. Loy

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In recent years, there have been several studies of various ’approximate’ versions of the key notion of amenability, which is defined for all Banach algebras; these studies began with work of Ghahramani and Loy in 2004. The present memoir continues such work: we shall define various notions of approximate amenability, and we shall discuss and extend the known background, which considers the relationships between different versions of approximate amenability. There are a number of open...

Amenability properties of Figà-Talamanca-Herz algebras on inverse semigroups

Hasan Pourmahmood-Aghababa (2016)

Studia Mathematica

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This paper continues the joint work with A. R. Medghalchi (2012) and the author’s recent work (2015). For an inverse semigroup S, it is shown that A p ( S ) has a bounded approximate identity if and only if l¹(S) is amenable (a generalization of Leptin’s theorem) and that A(S), the Fourier algebra of S, is operator amenable if and only if l¹(S) is amenable (a generalization of Ruan’s theorem).

Subtraction algebras and B C K -algebras

Young Hee Kim, Hee Sik Kim (2003)

Mathematica Bohemica

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In this note we show that a subtraction algebra is equivalent to an implicative B C K -algebra, and a subtraction semigroup is a special case of a B C I -semigroup.

Locally adequate semigroup algebras

Yingdan Ji, Yanfeng Luo (2016)

Open Mathematics

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We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J* 0 - 𝒥 * -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ* ℛ * -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we...

Connes amenability-like properties

Amin Mahmoodi (2014)

Studia Mathematica

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We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.

Is A - 1 an infinitesimal generator?

Hans Zwart (2007)

Banach Center Publications

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In this paper we study the question whether A - 1 is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by A - 1 . However, we construct a contraction semigroup with growth bound minus infinity for which A - 1 does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its...

Approximate diagonals and Følner conditions for amenable group and semigroup algebras

Ross Stokke (2004)

Studia Mathematica

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We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally...

Character pseudo-amenability of Banach algebras

Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

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Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.

A -systems

R. Gorton (1976)

Compositio Mathematica

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On the semilinear integro-differential nonlocal Cauchy problem

Piotr Majcher, Magdalena Roszak (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem x ' ( t ) + A x ( t ) = f ( t , x ( t ) , ∫ t ₀ t k ( t , s , x ( s ) ) d s ) , x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator T ( t ) t > 0 on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.