Related papers: Banach lattices with upper $p$-estimates: Renormin…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
This article gives a new proof of the fundamental lemma of the "weakly admissible implies admissible" theorem of Colmez-Fontaine that describes the semi-stable p-adic representations. To this end, we introduce the category of spectral…
In this paper, we study the coarse Lipschitz geometry of Banach spaces with several asymptotic properties. Specifically, we look at asymptotically uniformly smoothness and convexity, and several distinct Banach-Saks-like properties. Among…
It is proved that the linearity of metric projections on subspaces and the convexity of the polars of the convex cones in the uniformly convex and uniformly smooth Banach space are equivalent, and both of them is equivalent with the fact…
We study model-theoretic stability and independence in Banach lattices of the form $L_p(X,U,\mu)$, where $1 \leq p < \infty$. We characterize non-dividing using concepts from analysis and show that canonical bases exist as tuples of real…
We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier's power functions bounds $t^p$, with $p \geq 2$, and they are related to the notion…
We study certain interpolation and extension properties of the space of regular operators between two Banach lattices. Let $R_p$ be the space of all the regular (or equivalently order bounded) operators on $L_p$ equipped with the regular…
Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences…
Using upper $\ell_p$-estimates for normalized weakly null sequence images, we describe a new family of operator ideals $\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$ and $1\leq\xi\leq\omega_1$. These classes…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
We study the relation between primariness of Banach spaces and the stronger operator-theoretic notions of the primary factorisation property (PFP) and the uniform primary factorisation property (UPFP). We revisit several classical…
We study the class of $(p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…
We study two related quantities which generalize the concept of upper Banach density of a set to two measurable subsets of the plane. The first of them allows us to generalize a classic result on sufficiently large distances realized in a…
We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$, where $1<p\kll\infty$. \[ vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p' \pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl.\] This result is extended to Banach…
For $1< p <2$ we obtain sharp inequalities for the supremum of products of homogeneous polynomials on $L_p(\mu)$, whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in the…
Understanding the complemented subspaces of $L_p$ has been an interesting topic of research in Banach space theory since 1960. 1999, Alspach proposed a systematic approach to classifying the subspaces of $L_p$ by introducing a norm given by…
We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively…
When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…