Our aim is to give an explicit description of the Arens-Michael envelope for universal enveloping algebra a finite-dimensional nilpotent complex Lie algebra. It turns out that belongs class completions introduced by R.~Goodman in 70s. To find precise form this we preliminary characterize set holomorphic functions exponential type on simply connected group. This approach leads unexpected connect...

Let S(0,1) be the *-algebra of all classes Lebesgue measurable functions on unit interval (0,1) and let a complete symmetric Δ-normed *-subalgebra S(0,1), in which simple are dense, e.g., L∞(0,1), Llog(0,1), Arens algebra Lω(0,1) equipped with their natural Δ-norms. We show that there exists no non-trivial derivation commuting dyadic translations interval. type II (or I∞) von Neumann algebra, a...

A first checklist of the Iranian Chrysididae is proposed. The list includes 184 species in 20 genera. Seventy species and genera Spinolia Dahlbom, 1854, Spintharina Semenov, 1892, Trichrysis Lichtenstein, 1876 are newly recorded from Iran. New combination is proposed for Chrysura laconiae (Arens, 2001), comb. nov. (from Chrysis) and Chrysurapyrogaster turca (Linsenmaier, 1997), comb. nov. (from...

In this paper we shall study the multipliers on Banach algebras and We prove some results concerning Arens regularity and amenability of the Banach algebra M(A) of all multipliers on a given Banach algebra A. We also show that, under special hypotheses, each Jordan multiplier on a Banach algebra without order is a multiplier. Finally, we present some applications of m...

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...