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Displaying similar documents to “Perturbed linear rough differential equations”

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...

Operator algebras

T. K. Carne (1979-1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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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.

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.

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.

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...

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...

Non-normal elements in Banach *-algebras

B. Yood (2004)

Studia Mathematica

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Let A be a Banach *-algebra with an identity, continuous involution, center Z and set of self-adjoint elements Σ. Let h ∈ Σ. The set of v ∈ Σ such that (h + iv)ⁿ is normal for no positive integer n is dense in Σ if and only if h ∉ Z. The case where A has no identity is also treated.

Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

E. Kaniuth, A. T. Lau, A. Ülger (2007)

Studia Mathematica

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Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms...

Commutators in Banach *-algebras

Bertram Yood (2008)

Studia Mathematica

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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.

Normed "upper interval" algebras without nontrivial closed subalgebras

C. J. Read (2005)

Studia Mathematica

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It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed...

Banach's school and topological algebras

Wiesław Żelazko (2009)

Banach Center Publications

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We present here some evidence of the activity of Banach Lwów School of functional analysis in the field of topological algebras. We shall list several results connected with such names as Stanisław Mazur (1905-1981), Maks (Meier) Eidelheit (1910-1943), Stefan Banach (1892-1945) and Andrzej Turowicz (1904-1989) showing that if the war had not interrupted this activity we could expect more interesting results in this direction.

An extremal problem in Banach algebras

Anders Olofsson (2001)

Studia Mathematica

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We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.

Multi-valued operators and fixed point theorems in Banach algebras

Bapur Chandra Dhage (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.