Related papers: Remarks on countable subadditivity

Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.

We prove an operator inequality that extends strong subadditivity of entropy: after taking a trace, the operator inequality becomes the strong subadditivity of entropy.

We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation.

We give an extension of the Fekete's Subadditive Lemma for a set of submultiplicative functionals on countable product of compact spaces. Our method can be considered as an unfolding of the ideas [1]Theorem 3.1 and our main result is an…

We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators $A$ and $B$, we prove that…

The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are…

If the tunnel number of a link $K$ is denoted $t(K)$, a pair of knots $K_1,K_2$ is said to be subadditive if $t(K_1)+t(K_2)>t(K_1 # K_2)$. We construct new examples of subadditive links.

In this note we answer a question concerning lineability of the set of non-absolutely summing operators.

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

In this paper we provide insight into the classes of strongly subadditive/superadditive functions by highlighting numerous new examples and new results.

An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…

Subaddivity type matrix inequalities for concave funcions and symetric norms are given.

We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the…

In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.

In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker…

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by…