A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg–Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley–Wiener–Schwartz theorem, and define a convolution Banach algebra.

The main purpose of this note is to observe that the celebrated theorem of Malliavin on the failure of spectral synthesis for the group algebra L{G) of a non compact locally compact abelian group G can be strengthened to get the failure of weak spectral synthesis (in the sense of Warner [7]) for £(G) and also for the "generalised group algebra" L{G, A). Let A be a commutative, semisimple, regul...

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that: (i) A ring homomorphism of a commutative C∗-algebra onto another commutative C∗-algebra with connected infinite Gelfand space is either linear or anti-linear. (ii) A ring automorphism of L1(R ) is either linear or anti-linear. (iii...

in this paper, we extend some propositions of banachalgebras into module actions and establish the relationships betweentopological centers of module actions. we introduce some newconcepts as                         -property and -property for banach modules and obtain some conclusions inthe topological center of module actions and arens regularity of banachalgebras.

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...

On the topology of the group of invertible elements – A Survey – The topological structure of the group of invertible elements in a unital Banach algebra (regular group for short) has attracted topologists from the very beginning of homotopy theory. Be it for its own sake simply to show the instrumental power of newly invented methods or because there were important applications, the most notab...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...