The two diffeomorphism invariant algebras introduced in Grosser M., Farkas E., Kunziger M., Steinbauer R., On the foundations of nonlinear generalized functions I, II, Mem. Amer. Math. Soc. 153 (2001), no. 729, 93 pp., are identical.

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes is...

We show that, in any unitary (commutative or not) Baire locally pseudo-convex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.

We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University....

The non-commutative torus $C^{*}({\mathbb{Z}}^n,\omega )$ is realized as the $C^{*}$-algebra of sections of a locally trivial $C^{*}$-algebra bundle over $\widehat{S_{\omega }}$ with fibres isomorphic to $C^{*}({\mathbb{Z}}^n/S_{\omega },{\omega }_1)$ for a totally skew multiplier ${\omega }_1$ on ${\mathbb{Z}}^n/S_{\omega }$. D. Poguntke [9] proved that $A_{\omega }$ is stably isomorphic to $C\left(\widehat{S_{\omega }}\right)\otimes C^{*}({\mathbb{Z}}^n/S_{\omega },{\omega }_1)\cong C\left(\widehat{S_{\omega }}\right)\otimes A_{\varphi }\otimes M_{kl}\left(ℂ\right)$ for a simple non-commutative torus $A_{\varphi }$ and an integer $kl$. It is well-known that a stable isomorphism of two separable $C^{*}$-algebras is equivalent to the existence of equivalence bimodule between them. We construct an $A_{\omega }$-$C\left(\widehat{S_{\omega }}\right)\otimes A_{\varphi }$-equivalence bimodule.

Let $𝒜={\left\{A_t\right\}}_{t\in G}$ and $ℬ={\left\{B_t\right\}}_{t\in G}$ be $C^{*}$-algebraic bundles over a finite group $G$. Let $C={⨁}_{t\in G}{A}_t$ and $D={⨁}_{t\in G}{B}_t$. Also, let $A=A_e$ and $B=B_e$, where $e$ is the unit element in $G$. We suppose that $C$ and $D$ are unital and $A$ and $B$ have the unit elements in $C$ and $D$, respectively. In this paper, we show that if there is an equivalence $𝒜-ℬ$-bundle over $G$ with some properties, then the unital inclusions of unital $C^{*}$-algebras $A\subset C$ and $B\subset D$ induced by $𝒜$ and $ℬ$ are strongly Morita equivalent. Also, we suppose that $𝒜$ and $ℬ$ are saturated and that $A^{\text{'}}\cap C=𝐂1$. We show that if $A\subset C$ and $B\subset D$...