L0/E A. Pe lczyński was the first to ask if locally convex subspaces E have this property. If E is locally bounded then we can find such an operator (Kalton Peck [2]). Peck Starbird [6] showed that this is also true when E is isomorphic to ω, the space of all real sequences. The goal of this paper is to show that if E is locally convex then we can complete the previous diagram. We will state so...

Let X be a linear space. A p-norm on X is a real-valued function on X with 0 < p ≤ 1, satisfying the following conditions: (i) ‖x‖p ≥ 0 and ‖x‖p = 0⇔ x = 0, (ii) ‖αx‖p = |α|p‖x‖p, (iii) ‖x+ y‖p ≤ ‖x‖p +‖y‖p for all x, y ∈ X and all scalars α. The pair (X ,‖,‖p) is called a p-normed space. It is a metric linear space with a translation invariant metric dp defined by dp(x, y)= ‖x− y‖p for all x, ...

This paper is concerned with the lifting of the closures of sets. If H is a topological vector space, G a subspace and A closed in G for the induced topology, under what conditions on A in G is it true that the closure of A is preserved in H, i.e., A is closed in HI In this paper a fundamental lifting proposition is proved. 'Preservation of closure' will prove to be a fruitful technique in obta...

A theorem due to Milutin [12] (see also [13]) asserts that for any two uncountable compact metric spaces Qt and Q2> t n e spaces of continuous real-valued functions C ^ ) and C(Q2) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then QQ^X) and C(Q2;X) are isomorphic. The purpose of this paper is to show that this conclusion is ...

A fixed point theorem of Hadzic [5] is generalized to locally convex spaces and the new result is applied to extend a recent result on invariant approximation of Jungck and Sessa [8] and Mukherjee and Som [11] for non-convex condition of domain and without affineness condition of mappings. Some known results [1], [6], [13] and [16] are also extended and improved. A property known as Property Γ ...

We examine the so-called three-space-stability for some classes of linear topological and locally convex spaces for which this problem has not been investigated.

Abstract The paper alluded to in the title contains following striking result: Let $I$ be unit interval and $\Delta$ Cantor set. If $X$ is a quasi Banach space containing no copy of $c_{0}$ which isomorphic closed subspace with basis $C(I,\,X)$ linearly homeomorphic $C(\Delta ,\, X)$ , then locally convex, i.e., space. We will show that Kalton result sharp by exhibiting non-locally convex space...