We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such is strictly finer than it turns every chain complete, rooted tree into Fréchet–Urysohn, compact topological space. show rôle of such in theory weakly Corson Valdivia compacta. In particular, give first example space T whose closed subspace Valdivia, yet not Corson. This answers question due to...

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Vald...

A basic sequence in a Banach space is called wide-(s) if it is bounded and dominates the summing basis. (Wide-(s) sequences were originally introduced by I. Singer, who termed them P ∗-sequences.) These sequences and their quantified versions, termed λ-wide-(s) sequences, are used to characterize various classes of operators between Banach spaces, such as the weakly compact, Tauberian, and supe...

Several new characterizations of Banach spaces containing a subspace isomorphic to , are obtained. These are applied to the question of when 1 embeds in the injective tensor product of two Banach spaces. Notations and terminology. All Banach spaces are taken as infinite dimensional, “subspace” means “closed linear subspace,” “operator” means “bounded linear operator.” If W is a subset of a Bana...

The weakly compact reflection principle Reflwcpκq states that κ is a weakly compact cardinal and every weakly compact subset of κ has a weakly compact proper initial segment. The weakly compact reflection principle at κ implies that κ is an ω-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that κ is pω ` 1qweakly compact. Moreover, we...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

We consider certain speed estimates for Krylov subspace methods (such as GMRES) when applied upon systems consisting of a compact operator K with small unstructured perturbation B. Information about the decay of singular values of K is also assumed. Our main result is that the Krylov method will perform initially at superlinear speed when applied upon such pre-conditioned system. However, with ...