The Generalized Theory of Perfect Riesz Spaces I.
The generalized three circle- and other convexity theorems with application to the construction of envelopes of holomorphy
The geometry of a closed form
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
The geometry of -spaces over atomless measure spaces and the Daugavet property.
The geometry of Markov diffusion generators
The geometry of the norms of the space of continuous functions.
The Gleason problem for , , .
The Gleason-Kahane-Zelazko theorem and function algebras
A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will...
The Gleason-Kahane-Żelazko theorem and its generalizations
This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?
The Gliding Hump Property in Vector Sequence Spaces.
The gradient method for non-differentiable operators in product Hilbert spaces and applications to elliptic systems of quasilinear differential equations.
The graph traces of finite graphs and applications to tracial states of -algebras.
The Graves theorem revisited.
The Grothendieck property for injective tensor products of Banach spaces
The group of automorphisms of is algebraically reflexive
We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of is [algebraically] reflexive if and only if is *-isomorphic to . For purely atomic measures, we show that the group of automorphisms (or isometries) of is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism group...
The group of invertible elements in a Banach algebra
The group of invertible elements of a commutative Banach algebra
The Group Property of the Invariant S of von Neumann Algebras.
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 sequence space. III.