Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C∗-algebras generated by “universal” row contractions associated with F+n , the free semigroup with n generators. This class of C ∗-algebras includes the Cuntz-Toeplitz algebra C∗(S1, . . . , Sn) (resp. C ∗(B1, . . . , Bn)) generated by the creation operators on the f...

This paper analyses the construction of the kernel graph of a non-synchronizing transformation semigroup and introduces the inverse synchronization problem. Given a transformation semigroup S ≤ Tn, we construct the kernel graph Gr(S) by saying v and w are adjacent, if there is no f ∈ S with vf = wf . The kernel graph is trivial or complete if the semigroup is a synchronizing semigroup or a perm...

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S = k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

We consider the semigroup Ext(A, B) of extensions of a separable C *-algebra A by a stable C *-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext −1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homoto...

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...