Related papers: Operator Space Structures on $\ell^1(n).$
We present a method for constructing bounded strictly singular non-compact operators on mixed Tsirelson spaces defined either by the families (A_n) or (S_n) of a certain class, as well as on spaces built on them, including hereditarily…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the…
We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions. We also prove the…
The main result is that a finite dimensional normed space embeds isometrically in $\ell_p$ if and only if it has a discrete Levy $p$-representation. This provides an alternative answer to a question raised by Pietch, and as a corollary, a…
Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz,…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
It is shown that every operator on (C[0,1]) which preserves a copy of an asymptotic (\ell_1) space, also preserves a copy of (C[0,1]).
Using the $ku$- and $BP$-theoretic versions of Astey's cobordism obstruction for the existence of smooth Euclidean embeddings of stably almost complex manifolds, we prove that, for $e$ greater than or equal to $\alpha(n)$--the number of…
The Grassmannian $V_2(\mathbb{R}^{n+2})$ of oriented 2-planes in $\mathbb R^{n+2}$ where $n\ge3$ carries a homogeneous parabolic contact structure of Grassmannian type. The main result of this article is that on $V_2(\mathbb{R}^{n+2})$…
The theme of the first two sections, is to prepare the framework of how from a ``complicated'' family of so called index models $I \in K_1$ we build many and/or complicated structures in a class $K_2$. The index models are…
It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…
In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this…
In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we…
We study algebras of bounded noncommutative (nc) functions on unit balls of operator spaces (nc operator balls) and on their subvarieties. Considering the example of the nc unit polydisk we show that these algebras, while having a natural…
We describe all isometries of the $q$-numerical radius on the space ${\mathcal K}(\mathcal H)$ of compact operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$.
We study a closed unbounded self-adoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECS). We build a suitable MAEC for (H,Q), prove it is aleph 0 stable up to perturbations and…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…