Related papers: Banach lattices with upper $p$-estimates: Renormin…

Henstock-type integrals are considered, for multifunctions taking values in the family of weakly compact and convex subsets of a Banach lattice $X$. The main tool to handle the multivalued case is a R{\aa}dstr\"om-type embedding theorem…

New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

We describe the surjective isometries of the unit sphere of real Schreier spaces of all orders and their $p$-convexifications, for $1 < p < \infty$. This description allows us to provide for those spaces a positive answer to a special case…

We show that if $1<p\neq 2<\infty$, then any isometry of the $p$-convexification of the combinatorial Banach space associated with a hereditary family of finite subsets of $\mathbb{N}$ containing the singletons is given by a signed…

Let $\mathcal{P}$ be a class of Banach spaces and let $T=\{T_\alpha\}_{\alpha\in A}$ be a set of metric spaces. We say that $T$ is a set of {\it test-spaces} for $\mathcal{P}$ if the following two conditions are equivalent: (1)…

A polarity notion for sets in a Banach space is introduced in such a way that the second polar of a set coincides with the smallest strongly convex set with respect to R that contains it. Strongly convex sets are characterized in terms of…

We introduce new weighted $L^p$-type spaces defined in terms of weight function matrices and characterize the inclusion relations in terms of the defining matrices. Moreover, we provide a detailed study concerning the coincidence with the…

We modify the very well known theory of normed spaces $(E, \norm)$ within functional analysis by considering a sequence $(\norm_n : n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$ for each $n\in\N$. Our theory is…

By generalizing a construction of Garling, for each $1\leqslant p<\infty$ and each normalized, nonincreasing sequence of positive numbers $w\in c_0\setminus\ell_1$ we exhibit an $\ell_p$-saturated, complementably homogeneous Banach space…

The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a…

We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…

We compute the operator $p$-norm of some $n\times n$ complex matrices, which can be seen as bounded linear operators on the $n$ dimensional Banach space $\ell^p(n)$. The notion of logarithmic affine matrices is defined, and for such a…

We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…

We augment the dimension of the Euclidean space by one and the Picard iteration of a contraction by a simple iteration on the real line such that the resulting iteration becomes monotone increasing and bounded with respect to the order…

In the setting of Banach lattices the weak (resp. positive) Grothendieck spaces have been defined. We localize such notions by defining new classes of sets that we study and compare with some quite related different classes. This allows us…

Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its relationship with other convergences. In particular, we…

In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is…

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where…