Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional equation and of the Cauchy–Jensen functional inequality in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Furthermore, using the fixed point method, we prove the Hyers–Ulam stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Published by Elsevier Ltd

We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the CuntzKrieger uniqueness theorem, and compute the K-groups of our algebras.

In this paper we use nonstandard analysis ([1], [10], [12]) to investigate injectability into C-algebras B which are infinitesimal hulls of hyperfinite dimensional internal C-algebras B. B is obtained from B by considering the subspace Fin(B) of elements with norm ≪ ∞ and identifying x, y ∈ Fin(B) whenever x − y has infinitesimal norm. Though B is a legitimate standard C-algebra, it is very lar...

The corona algebra M(A)/A contains essential information on the global structure of A, as demonstrated for instance by Busby theory. It is an interesting and surprisingly difficult task to determine the ideal structure of M(A)/A by means of the internal structure of A. Toward this end, we generalize Freudenthal’s classical theory of ends of topological spaces to a large class of C∗-algebras. Ho...

In this paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

We study certain principal actions on noncommutative C-algebras. Our main examples are the Zpand T-actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C-algebras with the Cuntz-Krieger algebras of directed graphs. A general result abou...

Multiplicities corresponding to irreducible characters are defined for reality-based algebras. These algebras with a distinguished basis include fusion rings, C-algebras, and the adjacency algebras of finite association schemes. The definition of multiplicity generalizes that for schemes. For a broad class of these structures, which includes the adjacency algebras, it is proved that if all the ...