This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.

For each finite semisimple tensor category, we associate a quantum group (face algebra) whose comodule category is equivalent to the original one, in a simple natural manner. To do this, we also give a generalization of the Tannaka-Krein duality, which assigns a face algebra for each tensor category equipped with an embedding into a certain kind of bimodule category.

We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa–Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa–Holm equation is integrable by the inverse spectral transform in the multi-peakon case.

For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.

We extend recent results by Pisier on K-subcouples, i.e. subcouples of an interpolation couple that preserve the K-functional (up to constants) and corresponding notions for quotient couples. Examples include interpolation (in the pointwise sense) and a reinter-pretation of the Adamyan-Arov-Krein theorem for Hankel operators.

We consider association schemes with d classes and the underlying BoseMesner algebra, A . Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of A , we prove some results over the Krein parameters of an association scheme.

We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The Coend of such a functor turns out to be a Hopf algebroid over this ring. Using a result of [4] we characterize a small abelian, locally finite rigid monoidal category as the category of rigid comodules over a transitive Hopf algebroid.

In 2013, Van Dam, Martin and Muzychuk constructed a cometric Q − antipodal 4-class association scheme from GQ of order ( t 2 , ) odd, which has hemisystem. this paper we characterize by its Krein array. The techniques are used involve the triple intersection numbers introduced Coolsaet Jurišić.

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to regular even order quasi-differential expression Shin-Zettl type. The characterization is stated in terms specially chosen basis for kernel maximal and employs description Friedrichs due Möller Zettl.

We present a dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in literature. As result, we develop complex version of prove generalized Krein-Rutman type theorems.