Related papers: The Uniform Classification of Banach Spaces
Using a technique of adjoining an order unit to a normed linear space, we have characterized strictly convex spaces among normed linear spaces and Hilbert spaces among strictly convex Banach spaces respectively. This leads to a…
The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…
We investigate intrinsic Baire classes of Banach spaces defined by Argyros, Godefroy and Rosenthal (2003). We introduce a construction, for any Banach space $X$ with a basis, of an $\ell_1$-saturated separable Banach space $Y$ such that for…
This is an unpublished manuscript written in 1983-4. It contains several results about lattices (=integral quadratic forms) including the classification of the unimodular lattices in dimensions up to 25 and the construction of unimodular…
The paper is a complement to the survey: M.I.Ostrovskii "To\-po\-lo\-gies on the set of all subspaces of a Banach space and related questions of Banach space geometry", Quaestiones Math. (to appear). It contains proofs of some results on…
The category $Ban$ of Banach spaces and linear maps of norm $\leq 1$ is locally $\aleph_1$-presentable but not locally finitely presentable. We prove, however, that $Ban$ is locally finitely presentable in the enriched sense over complete…
We show that every metric space with bounded geometry uniformly embeds into an explicit reflexive Banach space (a direct sum of l^p spaces). In the case of discrete groups we show the analogue of a-T-menability. That is, we construct a…
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of…
The converse of Fortin's Lemma in Banach spaces is established in this Note.
This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…
We set up a descriptive set-theoretic framework to study Lipschitz-free spaces and use the reduction argument of Bossard to prove several results. We prove two universality results: if a separable Banach space is isomorphically universal…
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks…
Certain previously known upper bounds on the moments of the norm of martingales in 2-smooth Banach spaces are improved. Some of these improvements hold even for sums of independent real-valued random variables. Applications to concentration…
In this paper, we study Auerbach basis of the Banach spaces $l^n_p$. We provide a complete classification of the spaces in terms of the cardinality of their bases. We also give a complete description of these bases for $l^3_p$ ($l^2_p$ is…
In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove…
We investigate the connections between UC and UC* properties for ordered pairs of subsets (A,B) in metric spaces, which are involved in the study of existence and uniqueness of best proximity points. We show that the $UC^{*}$ property is…
In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the…
Henstock-type integrals are considered, for functions defined in a Radon measure space and taking values in a Banach lattice X considering the norm and the order structure of the space. A number of results are obtained, highlighting the…