There are two basic angles associated with a pair of linear subspaces: the Diximier angle and Friedrichs angle. These classical notions, which date back to first half 20th century, have been thoroughly studied due their utility in description convergence rates for various projection-based algorithms solving feasibility problems. The Dixmier orthogonal complements is same as original provided ...

This article investigates the notions of exposed points and (exposed) faces in matrix convex setting. Matrix finite dimensions were first defined by Kriel 2019. Here this notion is extended to sets infinite-dimensional vector spaces. Then a connection between extreme established: point ordinary if only it exposed. leads Krein-Milman type result for that due Straszewicz-Klee classical convexity:...

Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on real line with finite Poisson integral. We further develop this area by giving description whose have logarithmic integral converging over line. This result can be viewed as version classical Szego theorem in polynomials orthogonal unit c...

In this note we will present an extension of the Krein-Rutman theorem for an abstract non-linear, compact, positively 1-homogeneous operators on a Banach space having the properties of being increasing with respect to a convex cone K and such that there is a non-zero u ∈ K for which M Tu < u for some positive constant M . This will provide a uniform framework for recovering the Krein-Rutman-lik...

We study Toeplitz operators on the Hardy spaces of connected compact abelian groups and of tube-type bounded symmetric domains. A representation theorem for these operators and for classes of abstract Toeplitz elements in C*-algebras is proved. This is used to give a unified treatment to index theory in this setting, and a variety of new index theorems are proved that generalize the Gohberg–Kre...

We give a simpler proof of the Gromov–Milman theorem on concentration phenomenon on uniformly convex sphere. We also outline Rohlin’s theory of measurable partitions used in the proof. The purpose of this note is to present a localization technique for the sphere S on an example of the Gromov–Milman theorem [Gr-M] about the concentration phenomenon on uniformly convex spheres. This result was o...