We show that the unit ball of a full Hilbert C∗-module is sequentially compact in a certain weak topology if and only if the underlying C∗-algebra is finite dimensional. This provides an answer to the question posed in J. Chmieliński et al [Perturbation of the Wigner equation in inner product C∗-modules, J. Math. Phys. 49 (2008), no. 3, 033519].

in this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

Real inner product. Let V be a vector space over R. A (real) inner product is a function 〈−,−〉 : V × V → R such that • 〈x, y〉 = 〈y, x〉 for all x, y ∈ V, • 〈c1x1 + c2x2, y〉 = c1〈x1, y〉+ c2〈x2, y〉 for all x1, x2, y ∈ V, c1, c2 ∈ R, • 〈x, x〉 ≥ 0 with 〈x, x〉 = 0 iff x = 0. That is, the pairing is symmetric, linear in the first variable (and therefore bilinear, by symmetry), and positive definite. E...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

The configuration of regular 3-forms in dimension 6 is generalized to n-forms in dimension 2n. The algebras of complex, paracomplex, and dual numbers are systematically used. The automorphism groups of all forms are determined. In the last decade there has arisen interest in exterior forms of higher degree, first of all in forms of degree 3 (see [2] and [3]). It is known (see [4] and [1]) that ...

Let X be a finite subset of Euclidean space R. We define for each x ∈ X, B(x) := {(x, y) | y ∈ X, x 6= y, (x, x) ≥ (y, y)} where (, ) denotes the standard inner product. X is called an inside s-inner product set if |B(x)| ≤ s for all x ∈ X. In this paper, we prove that the cardinalities of inside s-inner product sets have the Fisher type upper bound. An inside s-inner product set is said to be ...