Related papers: A note on causality in Banach spaces

We show that on the unit ball of a certain separable Banach space there is a smooth delbar-closed (0,1)-form which is not locally delbar-exact. Further, the Dolbeault isomorphism theorem does not generalize to arbitrary Banach spaces.…

A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be…

In this work, we prove that linear bounded operators $T$ on a Banach space $X$ allowing spectral cuts along rectifiable Jordan curves meeting their spectrum are related to classes of operators admitting an unconventional functional…

Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…

It was recently shown in [24] that the Banach space operator relations Equivalence After Extension (EAE) and Schur Coupling (SC) do not coincide by characterizing these relations for operators acting on essentially incomparable Banach…

In our work, we provide a constructive proof of a generalized version of Cantor's diagonal argument for nets. This result expands the well-known technique beyond sequences, allowing it to be applied to a broader context. This result has…

We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a…

The use of a tensor product perspective has enriched functional analysis and other important areas of mathematics and physics. The context of operator spaces is clearly no exception. The aim of this manuscript is to kick off the development…

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is…

A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…

Let $X$ and $Y$ be Banach spaces, $A\,:\,X\rightarrow Y$ and $B,\,C\,:\,Y\rightarrow X$ be bounded linear operators. We prove that if $A(BA)^2=ABACA=ACABA=(AC)^2A,$ then $$\sigma_{*}(AC)\setminus\{0\}=\sigma_{*}(BA)\setminus\{0\}$$ where…

In this paper we provide a notion of causality for the violation of general Linear Temporal Logic (LTL) properties. The current work is a natural extension of the previously proposed approach handling causality in the context of…

We define the eigenderivatives of a linear operator on any real or complex Banach space, and give a sufficient condition for their existence.

The concept of causal abstraction got recently popularised to demystify the opaque decision-making processes of machine learning models; in short, a neural network can be abstracted as a higher-level algorithm if there exists a function…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…

The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. It is pointed out that Nimtz and coworkers use the notion of signal velocity in a different sense from Einstein…

We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…

We prove that, in a large class of Banach lattices, the fixed space of each commuting family of positive linear contractions is a lattice subspace. As consequences, new cyclicity results for the peripheral point spectra of positive…

In the paper we discuss conformable derivative behavior in arbitrary Banach spaces and clear the connection between two conformable derivatives of different order. As a consequence we obtain the important result that an abstract function…

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…