The equicontinuous week* topology and semi-reflexivity
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The equivalence of some Banach space problems
The exactness of the projective limit functor on the category of quotients of Frechet spaces
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
The Facial Q-Topology for Compact Convex Sets.
The facial structure of the finite dimensional latticial cone.
The fascinating homotopy structure of Sobolev spaces
We discuss recent developments in the study of the homotopy classes for the Sobolev spaces . In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].
The Finest Nachbin Topology is a Mixed Topology.
The Fréchet space admits a strictly stronger separable and quasicomplete locally convex topology
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The Generalized Theory of Perfect Riesz Spaces I.
The Gliding Hump Property in Vector Sequence Spaces.
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The Hahn-Banach property and equivalent conditions
The Hahn-Banach theorem implies the Banach-Tarski paradox
The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
The Hahn-Banach Theorem surveyed [Book]
The Hahn-Banach-Kantorovich formula for a lattice subdifferential.
The holomorphic functional calculus as an operational calculus
The Hypercyclicity Criterion for sequences of operators
We show that under no hypotheses on the density of the ranges of the mappings involved, an almost-commuting sequence (Tₙ) of operators on an F-space X satisfies the Hypercyclicity Criterion if and only if it has a hereditarily hypercyclic subsequence , and if and only if the sequence (Tₙ ⊕ Tₙ) is hypercyclic on X × X. This strengthens and extends a recent result due to Bès and Peris. We also find a new characterization of the Hypercyclicity Criterion in terms of a condition introduced by Godefroy...