Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when $$\alpha $$ is a group homomorphism which pushes forward the Haar measure G to absolutely continuous with respect on H, then $$(\alpha \times \alpha )^{-1}$$ preserves sets compact operator synthesis, and conversely onto. also similar preservation results for Ditkin M-sets, obtaining...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

A k-matching M of a graph G = (V,E) is subset ⊆ E such that each connected component in the subgraph F (V,M) either single-vertex or k-regular, i.e., vertex has degree k. In this contribution, we are interested k-matchings four standard products: Cartesian, strong, direct and lexicographic product. As shall see, problem finding non-empty (k ≥ 3) products NP-complete. Due to general intractabili...

1. [10 points] Determine whether the following statements are true or false (you have to include proofs/counterexamples): (a) Let R be an integral domain, F – a free R-module of finite rank, and M – a torsion R-module. Then there is no injective homomorphism from F to M . Solution: True. Suppose there was an injective homomorpism φ : F → M . Then let N = φ(F ); N is a submodule of M , and there...

Recent work of M. Yoshinaga [13] shows that in some instances certain higher homotopy groups of arrangements map onto non-resonant homology. This is in contrast to the usual Hurewicz map to untwisted homology, which is always the zero homomorphism in degree greater than one. In this work we examine this dichotomy, generalizing both results.

We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an equivariant closed form within its cohomological class to a form more suitable to yield localization results. This work is motivated by our work [5] on reproving wall crossing formulas in Seiberg-Witten theory, where t...