On Theorems of de Pagter and Ando-Krieger.
On three problems from the Scottish Book connected with orthogonal systems
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 two classes of Banach spaces with uniform normal structure
On Two Classes of Mappings on Banach Sequenee Spaces.
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 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...
On ultrapowers of linear topological spaces without convexity conditions.
On unconditional convergence of series in Banach lattices
On unconditional polynomial bases of the space
On unconditionally saturated Banach spaces
We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set 𝓐, in the Effros-Borel space of subspaces of C[0,1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y, with a Schauder basis, that contains isomorphic copies of every space X in the class 𝓐.
On uncountable unconditional bases in Banach spaces
On ∆-uniform convexity and drop property
On uniform Kadec–Klee properties and rotundity in generalized Cesàro sequence spaces.
On Uniformly Convex and Uniformly Kadec-Klee Renomings
We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces...
On uniformly Gâteaux smooth -smooth norms on separable Banach spaces
Every separable Banach space with -smooth norm (Lipschitz bump function) admits an equivalent norm (a Lipschitz bump function) which is both uniformly Gâteaux smooth and -smooth. If a Banach space admits a uniformly Gâteaux smooth bump function, then it admits an equivalent uniformly Gâteaux smooth norm.
On uniformly nonsquare points and nonsquare points of Orlicz spaces
For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.
On uniqueness of distribution of a random variable whose independent copies span a subspace in
Let 1 ≤ p < 2 and let be the classical -space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable spans in a subspace isomorphic to some Orlicz sequence space . We give precise connections between M and f and establish conditions under which the distribution of a random variable whose independent copies span in is essentially unique.
On unit balls and isoperimetrices in normed spaces
The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.
On Universal separable reflexive stable spaces