Displaying similar documents to “Operator algebras”

Some homological properties of Banach algebras associated with locally compact groups

Mehdi Nemati (2015)

Colloquium Mathematicae

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We investigate some homological notions of Banach algebras. In particular, for a locally compact group G we characterize the most important properties of G in terms of some homological properties of certain Banach algebras related to this group. Finally, we use these results to study generalized biflatness and biprojectivity of certain products of Segal algebras on G.

Invertibility in tensor products of Q-algebras

Seán Dineen, Pablo Sevilla-Peris (2002)

Studia Mathematica

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We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.

Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

Perturbed linear rough differential equations

Laure Coutin, Antoine Lejay (2014)

Annales mathématiques Blaise Pascal

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We study linear rough differential equations and we solve perturbed linear rough differential equations using the Duhamel principle. These results provide us with a key technical point to study the regularity of the differential of the Itô map in a subsequent article. Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach algebras more general than tensor algebras and to consider extensions of classical results such...

Tensor products of partial algebras.

Miquel Monserrat, Francesc Roselló, Joan Torrens (1992)

Publicacions Matemàtiques

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In this paper we introduce the tensor product of partial algebras w.r.t. a quasi-primitive class of partial algebras, and we prove some of its main properties. This construction generalizes the well-known tensor product of total algebras w.r.t. varieties.

On φ-inner amenable Banach algebras

A. Jabbari, T. Mehdi Abad, M. Zaman Abadi (2011)

Colloquium Mathematicae

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Generalizing the concept of inner amenability for Lau algebras, we define and study the notion of φ-inner amenability of any Banach algebra A, where φ is a homomorphism from A onto ℂ. Several characterizations of φ-inner amenable Banach algebras are given.

Amenability for dual Banach algebras

V. Runde (2001)

Studia Mathematica

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We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions...

Approximate identities in Banach function algebras

H. G. Dales, A. Ülger (2015)

Studia Mathematica

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In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to...

Solved and unsolved problems in generalized notions of amenability for Banach algebras

Yong Zhang (2010)

Banach Center Publications

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We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.

Vector space isomorphisms of non-unital reduced Banach *-algebras

Rachid ElHarti, Mohamed Mabrouk (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras...