n this paper we study the hyers-ulam-rassias stability of cauchyequation in felbin's type fuzzy normed linear spaces. as a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. this shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map ...

Let *3* be the algebra of polynomials in one indeterminate x over the complex field C. Suppose || • || is a norm on 9 such that the coefficient functionals c,: X a.oc' —* a, (j = 0,1,2, • • •) are all continuous with respect to || • ||, and let K CC be the set of characters on 9> which are || • ||-continuous. Then K is compact, C\K is connected, and 0 G K. Let A be the completion of 9 with resp...

Let A be a finite-dimensional algebra over the complex numbers with nonzero identity element e. If x ∈ A, then the resolvent set associated to x is the set ρ(x) of complex numbers λ such that λ e − x is invertible, and the spectrum of x is the set σ(x) of complex numbers λ such that λ e − x is not invertible. For instance, if V is a finite-dimensional vector space over the complex numbers of po...

We show that, for every ultraprime Banach algebra A, there exists a positive number γ satisfying γ‖a+Z(A)‖ ≤ ‖Da‖ for all a in A, where Z(A) denotes the centre of A and Da denotes the inner derivation on A induced by a. Moreover, the number γ depends only on the “constant of ultraprimeness” of A.

It is shown that a) it is possible to define the topology of any topological algebra by a collection of F -seminorms, b) every complete locally uniformly absorbent (complete locally A-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, A-(k-normed) algebras, where k ∈ (0, 1] varies, c) every complete...

This paper is concerned with the description of exceptional simple Lie algebras as octonionic analogues of the classical matrix Lie algebras. We review the Tits-Freudenthal construction of the magic square, which includes the exceptional Lie algebras as the octonionic case of a construction in terms of a Jordan algebra of hermitian 3× 3 matrices (Tits) or various plane and other geometries (Fre...

In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We...

We present a short and rather self-contained introduction to the theory of finite dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In sections 2–3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra ...

The classical Mazur–Ulam theorem which states that every sur-jective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.