相关论文: Normal tilings of a Banach space and its ball

Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric…

We say that a triangle $T$ tiles a polygon $A$, if $A$ can be dissected into finitely many nonoverlapping triangles similar to $T$. We show that if $N>42$, then there are at most three nonsimilar triangles $T$ such that the angles of $T$…

We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique…

We say that a smooth normed space $X$ has a property (SL), if every mapping $f:X \to X$ preserving the semi-inner product on $X$ is linear. It is well known that every Hilbert space has the property (SL) and the same is true for every…

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banach spaces with the uniform approximation property. This generalizes a…

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class…

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…

It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infinite dimensions, little progress has been made since Klee…

We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This…

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…

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable…

We find a natural class of transformations ("flattened perturbations") of a norming M-basis in a Banach space X, which give a strong norming M-basis in X. This simplifies and generalizes the positive answer to the "strong M-basis problem"…

A famous problem in discrete geometry is to find all monohedral plane tilers, which is still open to the best of our knowledge. This paper concerns with one of its variants that to determine all convex polyhedra whose every cross-section…

The main result: the dual of separable Banach space $X$ contains a total subspace which is not norming over any infinite dimensional subspace of $X$ if and only if $X$ has a nonquasireflexive quotient space with the strictly singular…

The paper elucidates the relationship between the density of a Banach space and possible sizes of well-separated subsets of its unit sphere. For example, it is proved that for a large enough space $X$, the unit sphere $S_X$ always contains…

Every normal periodic tiling is a strongly balanced tiling. The properties of periodic tilings by convex polygons are rearranged from the knowledge of strongly balanced tilings. From the results, we show the properties of representative…

We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…

According to a result due to B.T. Polyak, a mapping between Hilbert spaces, which is $C^{1,1}$ around a regular point, carries a ball centered at that point to a convex set, provided that the radius of the ball is small enough. The present…

We prove that the following three properties for a Banach space are all different from each other: every finite convex combination of slices of the unit ball is (1) relatively weakly open, (2) has nonempty interior in relative weak topology…

We show how to construct nonlocally convex quasi-Banach spaces $X$ whose dual separates the points of a dense subspace of $X$ but does not separate the points of $X$. Our examples connect with a question raised by Pietsch [About the Banach…