Small operators between Banach and Hilbert spaces
Some fixed point theorems for nonconvex spaces.
Some new classes of topological vector spaces with closed graph theorems
In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.
Some Properties of Hausdorff Measure of Noncompactness on Locally Bounded Topological Vector Spaces
Some Ramsey type theorems for normed and quasinormed spaces
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Stability of the Cauchy functional equation in quasi-Banach spaces
Let X be a quasi-Banach space. We prove that there exists K > 0 such that for every function w:ℝ → X satisfying ||w(s+t)-w(s)-w(t)|| ≤ ε(|s|+|t|) for s,t ∈ ℝ, there exists a unique additive function a:ℝ → X such that a(1)=0 and ||w(s)-a(s)-sθ(log₂|s|)|| ≤ Kε|s| for s ∈ ℝ, where θ: ℝ → X is defined by for k ∈ ℤ and extended in a piecewise linear way over the rest of ℝ.
Stability of the method of least squares for finding the eigenvalues of a symmetric operator
Strong reflexivity of Abelian groups
A reflexive topological group is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.
Subspaces of for that are admissible as kernels.
Symmetric -normed space for