in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

let s be a locally compact foundation semigroup with identity and                          be its semigroup algebra. let x be a weak*-closed left translation invariant subspace of    in this paper, we prove that  x  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. we also prove that a foundation semigroup with identity s is left amenab...

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

Optimal hypercontractivity bounds for the fermion oscillator semigroup are obtained. These are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained by Nelson. In the process, several results of independent interest in the theory of non-commutative integration are established. ∗ On leave from School of Math., Georgia Institute of Technology, At...

We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...