Character Amenability of Lipschitz Algebras

2014 ◽  
Vol 57 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Mahshid Dashti ◽  
Rasoul Nasr-Isfahani ◽  
Sima Soltani Renani
Keyword(s):  
Metric Space ◽  
Banach Algebras ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Character Amenability

AbstractLet be a locally compact metric space and let 𝒜 be any of the Lipschitz algebras , , or . In this paper, we show, as a consequence of rather more general results on Banach algebras, that 𝒜 is C-character amenable if and only if is uniformly discrete.

Amenability of Banach algebras

1989 ◽  
Vol 105 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Frédéric Gourdeau
Keyword(s):  
Banach Algebra ◽  
Metric Space ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Commutative Banach Algebra ◽  
Cohomology Theory ◽  
Compact Metric Space ◽  
Amenable Banach Algebra ◽  
Second Dual

We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1].

Horseshoes and the Conley index spectrum

2000 ◽  
Vol 20 (2) ◽  
pp. 365-377 ◽  
Author(s):  
MARIA C. CARBINATTO ◽  
JAROSLAW KWAPISZ ◽  
KONSTANTIN MISCHAIKOW
Keyword(s):  
Metric Space ◽  
Conley Index ◽  
Spectral Information ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Continuous Map ◽  
Full Shift ◽  
Shift Dynamics ◽  
Isolating Neighborhood

Given a continuous map on a locally compact metric space and an isolating neighborhood which is decomposed into two disjoint isolating neighborhoods, it is shown that the spectral information of the associated Conley indices is sufficient to conclude the existence of a semi-conjugacy onto the full shift dynamics on two symbols.

A Denoised Version of Some Kinds of Set Convergence

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Filomena A. Lops
Keyword(s):  
Hausdorff Measure ◽  
Metric Space ◽  
Lower Semicontinuity ◽  
Set Convergence ◽  
Minimizing Sequence ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Compactness Result ◽  
Hausdorff Convergence ◽  
Kuratowski Convergence

AbstractThe aim of this paper consists of introducing on a locally compact and σ-compact metric space a notion of set convergence, which generalizes the Hausdorff convergence, the local Hausdorff convergence and the Kuratowski convergence. We analyze the connections beetwen the three new notions: and. in particular, we prove a compactness result. As a first application of this convergence we give, on a sequence of sets, a condition which assures the lower semicontinuity of the Hausdorff measure with respect to this new convergence and we show that this condition is satisfied by any minimizing sequence of Mumford-Shah functional.

scholarly journals Regional topology and approximative solutions of difference and differential equations

2015 ◽  
Vol 63 (1) ◽  
pp. 183-203 ◽  
Author(s):  
Janusz Migda
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Point Theorem ◽  
Metric Space ◽  
Schauder’S Fixed Point Theorem ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Real Functions

Abstract We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain new versions of Schauder’s fixed point theorem and Ascoli’s theorem. We use these theorems and the properties of the iterated remainder operator to establish conditions under which there exist solutions, with prescribed asymptotic behaviour, of some difference and differential equations.

scholarly journals ESSENTIAL CHARACTER AMENABILITY OF BANACH ALGEBRAS

2011 ◽  
Vol 84 (3) ◽  
pp. 372-386 ◽  
Author(s):  
RASOUL NASR-ISFAHANI ◽  
MEHDI NEMATI
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Cambridge Philos ◽  
Character Amenability

AbstractFor a Banach algebra 𝒜 and a character ϕ on 𝒜, we introduce and study the notion of essential ϕ-amenability of 𝒜. We give some examples to show that the class of essentially ϕ-amenable Banach algebras is larger than that of ϕ-amenable Banach algebras introduced by Kaniuth et al. [‘On ϕ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc.144 (2008), 85–96]. Finally, we characterize the essential ϕ-amenability of various Banach algebras related to locally compact groups.

scholarly journals On the uniform exponential stability of linear skew-product semiflows

2006 ◽  
Vol 4 (2) ◽  
pp. 145-161
Author(s):  
Ciprian Preda
Keyword(s):  
Exponential Stability ◽  
Large Class ◽  
Metric Space ◽  
Orlicz Spaces ◽  
Skew Product ◽  
Test Functions ◽  
Type Condition ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Uniform Exponential Stability

The problem of uniform exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers, is discussed. It is established a connection between the uniform exponential stability of linear skewproduct semiflows and some admissibility-type condition. This approach is based on the method of “test functions”, using a very large class of function spaces, the so-called Orlicz spaces.

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