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...

Communicated by Abstract. We will prove that, if every finite dimensional subspace of an infinite dimensional operator space E is 1-completely complemented in it, E is 1-Hilbertian and 1-homogeneous. However, this is not true for finite dimensional operator spaces: we give an example of an n-dimensional operator space E, such that all of its subspaces are 1-completely complemented in E, but whi...

The complemented subspace problem asks, in general, which closed subspaces M of a Banach space X are complemented; i.e. there exists a closed subspace N of X such that X = M ⊕ N? This problem is in the heart of the theory of Banach spaces and plays a key role in the development of the Banach space theory. Our aim is to investigate some new results on complemented subspaces, to present a history...

The complemented subspace problem asks, in general, which closed subspaces M of a Banach space X are complemented; i.e. there exists a closed subspace N of X such that X = M ⊕N? This problem is in the heart of the theory of Banach spaces and plays a key role in the development of the Banach space theory. Our aim is to investigate some new results on complemented subspaces, to present a history ...

It is shown that the span of fa i h i b i e i g n i=1 , where fh i g is the Haar system in L p and fe i g the canonical basis of`p , is well isomorphic to a well complemented subspace of L p ; 2 < p < 1. As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in L p ; 2 < p < 1, any block basis of which is well isomorphic to a well complemented subspac...

In this paper we continue the study of Lorentz sequence spaces d(w,p), 0 < p < 1, initiated by N. Popa [8]. First we show that the Mackey completion of d(w,p) is equal to d(v, 1) for some sequence v. Next, we prove that if d(w, p) (2 h, then it contains a complemented subspace isomorphic to lp. Finally we show that if limn_1(X)"=1 wi)1 = °°, tnen every complemented subspace of d(w,p) with symme...