We show that the class of subspaces of c0(N) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to c0(N) is linearly isomorphic to c0(N). The proof relies in part on an isomorphic characterization of subspaces of c0(N) as separable spaces having an equivalent norm such that the weak-star and norm topologies quantitatively agree on t...

We discuss the finite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classification of subspaces of ℓ n p .

The paper investigates free and projective L-spaces, where L is a given normed space. These spaces form far-reaching generalization of known p-multinormed spaces; in particular, if L=Lp(X), the L-spaces can be considered as spaces, based on arbitrary σ-finite measure X (for “canonical” X=N with counting measure). We first describe “naturally appearing” functor, paving contractively complemented...

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...

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 ...

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...