We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

We show that the Yang-Baxter equation is equivalent to the associativity of the algebra generated by non-commuting link operators. Starting from these link operators we build out the (FFZ) algebras, the slq(2) is derived by considering a special combination of the generators of (FFZ) algebra. MIRAMARE – TRIESTE September 1998 Junior Associate of the Abdus Salam ICTP. E-mail: [email protected] Regu...

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of set disjoint non-norm null weakly sequences and regular-polynomially in Banach lattices. Then apply mother vector ? ? ( E ) ? s $\lambda _\pi (E) \setminus \lambda _s(E)$ , which implies ? p ? ? | $(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell }_{\pi }E)$ where is lattice 1 < ? $1 \infty$ .

On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair coprime integers $(p,q)$ it was found numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ satisfying inequalities $\pi/3< \alpha_1 < \alpha_2 2\pi/3$ such that with faces angle $\alpha \in \left( \pi/3, \right)$ exists unique, up to rigid motion tetrahedron, geodesic type $(p,q...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

STUDY OBJECTIVE To assess whether the withdrawal of salmeterol treatment for 3 days (72 h) can restore its bronchoprotective ability on specific bronchial provocative test (sBPT) with allergen, which was completely lost after 1 week of regular treatment with salmeterol. STUDY DESIGN Single-blind design. PATIENTS AND METHODS We investigated 10 nonsmoking subjects (8 men and 2 women; mean +/-...

Protein phase separation is implicated in formation of membraneless organelles, signaling puncta and the nuclear pore. Multivalent interactions of modular binding domains and their target motifs can drive phase separation. However, forces promoting the more common phase separation of intrinsically disordered regions are less understood, with suggested roles for multivalent cation-pi, pi-pi, and...

Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...

We discuss the reduction of gravitating Chern-Simons electrodynamics with two commuting Killing vectors to a dynamical problem with four degrees of freedom, and present regular particle-like solutions. In three space-dimensions, the abelian Higgs model coupled to Einstein gravity is known to admit static multi-vortex solutions [1]. Stationary vortex solutions arise [2] when a Chern-Simons term ...