Related papers: On Linearity of Nonclassical Differentiation

By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…

A linear operator on a Hilbert space $\mathbb{H}$, in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be ommited by using a criterion for the graph of…

A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…

We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…

This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…

Let $X$ and $Y$ be compact Hausdorff spaces, $E$ and $F$ be real or complex Banach spaces, and $A(X,E)$ be a subspace of $C(X,E)$. In this paper we study linear operators $S,T: A(X,E) \lo C(Y,F)$ which are jointly separating, in the sense…

We study effectively inseparable (e.i.) pre-lattices (i.e. structures of the form $L=\langle \omega, \wedge, \lor, 0, 1, \leq_L\rangle$ where $\omega$ denotes the set of natural numbers and the following hold: $\wedge, \lor$ are binary…

The author studies the structure of space $ \mathbf {L} _ {2} (G) $ of vector-valued functions that are square integrable in a bounded connected domain $ G $ of the three-dimensional space with a smooth boundary and the role of gradient…

Divergence functions of a metric space estimate the length of a path connecting two points $A$, $B$ at distance $\le n$ avoiding a large enough ball around a third point $C$. We characterize groups with non-linear divergence functions as…

If $K$ is a compact Hausdorff space so that the Banach lattice $C(K)$ is isometrically lattice isomorphic to a dual of some Banach lattice, then $C(K)$ can be decomposed as the $\ell^\infty$-direct sum of the carriers of a maximal singular…

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

We introduce a notion of completely bounded holomorphic functions defined on the open unit ball of an operator space. We endow the set of these functions with an operator space structure, and in the scalar-valued case we identify an…

In this paper, a question due to Heckenberger, Shareshian and Welker on racks in [7] is positively answered. A rack is a set together with a selfdistributive bijective binary operation. We show that the lattice of subracks of every finite…

We define the notion of {\em rational presentation of a complete metric space} in order to study metric spaces from the algorithmic complexity point of view. In this setting, we study some presentations of the space $\czu$ of uniformly…

Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fr\'echet algebra L(s',s) of the so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s)…

We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…

Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…