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An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal…
Within convex analysis, a rich theory with various applications has been evolving since the proximal average of convex functions was first introduced over a decade ago. When one considers the subdifferential of the proximal average, a…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…
Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies and even images.…
This monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator…
Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379--1389] for computing optimal designs. A conjecture of…
The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the…
We introduce the notion of quasimonotone polar of a multivalued operator, in a similar way as the well-known monotone polar due to Martinez-Legaz and Svaiter. We first recover several properties similar to the monotone polar, including a…
We prove comparison principles for nonlinear potential theories in euclidian spaces in a very straightforward manner from duality and monotonicity. We shall also show how to deduce comparison principles for nonlinear differential operators,…
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in…
In the first part of the note we prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain and is maximal. Simons'…
In this notes unbounded regular operators on Hilbert $C^*$-modules over arbitrary $C^*$-algebras are discussed. A densely defined operator $t$ possesses an adjoint operator if the graph of $t$ is an orthogonal summand. Moreover, for a…
Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl--von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear…
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently…
In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both…