In this paper we give a short proof of the main results of Kumam, Dung and
Sitthithakerngkiet (P. Kumam, N.V. Dung, K. Sitthithakerngkiet, A
Generalization of Ciric Fixed Point Theorems, FILOMAT 29:7 (2015),
1549-1556).
AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.
In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.
We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].