On topologically nilpotent algebras
On Topologies In Ordered Vector Spaces.
On topologizable algebras
On topologization of countably generated algebras
We prove that any real or complex countably generated algebra has a complete locally convex topology making it a topological algebra. Assuming the continuum hypothesis, it is the best possible result expressed in terms of the cardinality of a set of generators. This result is a corollary to a theorem stating that a free algebra provided with the maximal locally convex topology is a topological algebra if and only if the number of variables is at most countable. As a byproduct we obtain an example...
On total incomparability of mixed Tsirelson spaces
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form with index finite are either or saturated for some and we characterize when any two spaces of such a form are totally incomparable in terms of the index and the parameter . Also, we give sufficient conditions of total incomparability for a particular class of spaces of the form in terms of the asymptotic behaviour of the sequence where is the canonical basis....
On Totally Barreled Spaces.
On transition multimeasures with values in a Banach space
On two classes of Banach spaces with uniform normal structure
On two classes of LF-spaces
On Two Classes of Mappings on Banach Sequenee Spaces.
On two classes of weighted Sobolev-Slobodetskiĭ spaces in a dihedral angle
On two new characterizations of Stieltjes transforms for distributions.
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
On two properties of Zorn type for locally convex spaces
On two quantum versions of the detailed balance condition
Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form (s ∈ [0,1]) in order...
On two reverse inequalities in the Segal-Bargmann space.
On two-points boundary value problems for ordinary nonlinear differential equations of the fourth order in the Colombeau algebra
On Typical Compact Convex Sets in Hilbert Spaces
Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.
On typical Markov operators acting on Borel measures.
On ultrapowers of Banach spaces of type
We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain c₀ complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs have been infected by that statement. In particular we provide proofs for the following statements: (i) All M-spaces, in particular all C(K)-spaces, have ultrapowers isomorphic to ultrapowers of c₀, as also do all their complemented subspaces isomorphic to their...