Related papers: Classifying Linear Matrix Inequalities via Abstrac…

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…

Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…

Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…

Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras. We…

This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that…

The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix…

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the…

Linear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unknowns are central to the theories of completely positive maps…

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator…

A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…

The linear-programming decoding performance of a binary linear code crucially depends on the structure of the fundamental cone of the parity-check matrix that describes the code. Towards a better understanding of fundamental cones and the…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

We introduce two notions of coarse embeddability between operator spaces: almost complete coarse embeddability of bounded subsets and spherically-complete coarse embeddability. We provide examples showing that these notions are strictly…

We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…