In this paper, modifying the construction of a C∗-ternary algebra from a given C∗-algebra, we define a proper CQ∗-ternary algebra from a given proper CQ∗-algebra. We investigate homomorphisms in proper CQ∗-ternary algebras and derivations on proper CQ∗-ternary algebras associated with the Cauchy functional inequality ‖f(x) + f(y) + f(z)‖ ≤ ‖f(x+ y + z)‖. We moreover prove the Hyers-Ulam stabili...

We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also...

As a continuation of [7], we introduce the notions of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras and study some related properties. In the section 3, we investigate the compactness in a TBCI-algebra X and quotient TBCI-algebra X=I where I is a topological ideal of X. In the section 4, we introduce the notion of topological homomorphisms...

Let $\mathcal A$ be a unital $C^*$-algebra. We consider Jordan $*$-homomorphisms on $C(X, \mathcal A)$ and Lip$(X,\mathcal A)$. More precisely, for any $C^*$-algebra A$, we prove that every $*$-homomorph

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular W-algebras both in type A. The construction is given via coproduct and evaluation map for Yangians. As a consequence, we show that parabolic inductions representations can be regarded as tensor product under homomorphisms. same method applicable also super-setting.

Let B be a strictly real commutative real Banach algebra with the carrier space Φ B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ : A → B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A) is contained in the radical of B. 1. Introduction and results. Ring homomorphisms are mappings between two ...

Following E. Kirchberg, [3], we call a bifunctor (A,B) → A⊗α B a C -algebraic tensor product functor if it is obtained by completing of the algebraic tensor product A ⊙ B of C-algebras in a functional way with respect to a suitable C-norm ‖ · ‖α. We call such a functor symmetric if the standard isomorphism A ⊙ B ∼= B ⊙ A extends to an isomorphism A⊗αB ∼= B⊗αA. Similarly, we call it associative ...