The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, find a five term exact sequence corresponding to this invariant, and describe the role of the Bogomolov multiplier in the theory of central extensions. A new description of the Bogomolov multiplier of a nilpotent group of class two is obtained. We define the Bogomolov multiplier within K-theory and show that proving its triviality is equivalent to solving a long-standing problem posed by Bass. An algorithm for computing the Bogomolov multiplier is developed.
COBISS.SI-ID: 16521305
We prove an infinite-dimensional generalization of Zenger's lemma that was used in the proof of the fact that the convex hull of the point spectrum of a linear operator is contained in its numerical range. Two relevant examples are given, and possible application in the Arrow-Debreu model is also discussed.
COBISS.SI-ID: 16214617
In this paper, we show that if a band-irreducible, bounded linear operator ▫$T$▫ acting on ▫$L^p(X, \mu)$▫ sends positive functions to positive functions, then any proper compact band compression of ▫$T$▫ must have spectral radius strictly smaller than that of ▫$T$▫. This result is generalized to operators ▫$T$▫ for which some power of ▫$T$▫ is compact. We apply this to the study of the band triangularizability of positive compact operators whose diagonal expectations share certain spectral properties with the original operator.
COBISS.SI-ID: 16357721