let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.

Most of the tests of liver function normally performed in a routine laboratory depend on quantitative and qualitative changes in the serum proteins. Since it is now well established that the serum protein pattern in Africans differs significantly from that generally accepted as normal for Europeans (Arens and Brock, 1954; Edozien, 1957; Holmes, Stanier, Semambo, and Jones, 1951 ; Schofield, 195...

We denote by T 2 the torus: z = exp iθ, w = exp iφ, and we fix a positive irrational number α. Aα denotes the space of continuous functions f on T 2 whose Fourier coefficient sequence is supported by the lattice half-plane n + mα ≥ 0. R. Arens and I. Singer introduced and studied the space Aα, and it turned out to be an interesting generalization of the disk algebra. Here we construct a differe...

REFERENCES 1. Council Directive 80/778/EEC [European Economic Community] concerning the quality of drinking water intended for human consumption. July 15,1980. 2. Martin MV. The significance of the bacterial contamination of dental unit water systems. Br Dent J 1987;163:152-154. 3. Williams JF, Huntington MK, Johnston AM. Dental waterlines. A source of contamination. Infection Control and Steri...

Let K be a locally compact p-adic field, g a split reductive Lie algebra over K and U(g) its universal enveloping algebra. We investigate the category Cg of coadmissible modules over the p-adic Arens-Michael envelope Û(g) of U(g). Let p ⊆ g be a parabolic subalgebra. The main result gives a canonical equivalence between the classical parabolic BGG category of g relative to p and a certain expli...