Let A + B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h : X → A + B splits into a sum h = f + g of continuous mappings f : X → A and g : X → B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear ...

Abstract: This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator T on a Hilbert space with an orthogonal basis, we define the isomorphic structure Σ(T ) as the family of all subsets of the basis so that T restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of Σ(T ). It improve...

If a and b are elements of an algebra, then we show that ab is Drazin invertible if and only if ba is Drazin invertible. With this result we investigate products of bounded linear operators on Banach spaces. 1. Drazin inverses Throughout this section A is a real or complex algebra with identity e 6= 0. We denote the group of invertible elements of A by A. We call an element a ∈ A relatively reg...

Abstract. Calculation of Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for usual Ito-diffusions. In this article we prove existence of Malliavin weights for jump diffusions under Hörmander conditions and hypotheses on the invertibility of the linkage operators. The main result – in the hypo-ellitpic case – is the invertibility of the covariance matrix, which ...

Invertibility attack is a hostile measure to breach watermarking systems. In this paper, a novel watermarking protocol using a one-way hash function and a check of random watermarks is proposed in order to combat invertibility attacks. The described technique can be used in conjunction with any watermarking algorithm, no matter it is kept secret or made public, without resorting to a third part...

Under standard Lipschitz conditions, trajectories of systems described by ordinary differential equations are well defined in both forward and reverse time. (The flow map is invertible.) However for hybrid systems, uniqueness of trajectories in forward time does not guarantee flow-map invertibility, allowing non-uniqueness in reverse time. The paper establishes a necessary and sufficient condit...

This paper reports an algorithm to check for the invertibility of nullboundary three neighborhood cellular automata (CAs). While the best known result for checking invertibility is quadratic [1, 2], the complexity of the proposed algorithm is linear. An efficient data structure called a rule vector graph (RVG) is proposed to represent the global functionality of a cellular automaton (CA) by its...

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in