We develop a very general operator-valued functional calculus for operators with an Hâˆžâˆ’calculus.We then apply this to the joint functional calculus of two sectorial operators when one has anâ€¦ (More)

Let X be an F-space, and let Y be a subspace of X of dimension one, with X/Y = lp (0 p oo). Provided p ~ 1, X ~lp; however if p = 1, we construct an example to show that X need not be locally convex.â€¦ (More)

We study the structure of Lipschitz and HÃ¶lder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve aâ€¦ (More)

We show that the class of subspaces of c0(IN) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitzisomorphic to c0(IN) is linearly isomorphic toâ€¦ (More)

We answer a question of Peller by showing that for any c > 1 there exists a power-bounded operator T on a Hilbert space with the property that any operator S similar to T satisfies sup n â€–Snâ€– > c.

This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on RÃ—R. We show that this is not always the case. Moreover, we find necessaryâ€¦ (More)

We investigate the stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDEâ€™s and several applications are presented.

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelsonâ€¦ (More)

We show that there is no uniformly continuous selection of the quotient map Q : `âˆž â†’ `âˆž/c0 relative to the unit ball. We use this to construct an answer to a problem of Benyamini and Lindenstrauss;â€¦ (More)

We study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities. In particular, we obtain explicit criteria for theâ€¦ (More)