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 Continuity of the Spectral Radius in Banach Algebras.
On ∆-uniform convexity and drop property
On Uniform Differentiability
We introduce the notion of uniform Fréchet differentiability of mappings between Banach spaces, and we give some sufficient conditions for this property to hold.
On uniform Kadec–Klee properties and rotundity in generalized Cesàro sequence spaces.
On uniformly continuous operators and some weight-hyperbolic function Banach algebra.
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 unitary convex decompositions of vectors in a -algebra
By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital -algebra permits the vector decomposable as convex combination of fewer unitaries; certain -algebra results due to M. Rørdam have been extended to the general setting of -algebras.
On unitary equivalence of invariant subspaces of the Dirichlet space
It is shown that in the Dirichlet space , two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift are unitarily equivalent only if ℳ ₁ = ℳ ₂.
On unitary equivalence of quasi-free Hilbert modules
We characterize unitary equivalence of quasi-free Hilbert modules, which complements Douglas and Misra's earlier work [New York J. Math. 11 (2005)]. We first confine our arguments to the classical setting of reproducing Hilbert spaces and then relate our result to equivalence of Hermitian vector bundles.
On Universal separable reflexive stable spaces
On variation topology