In this paper, we show that if an injective map  on symmetric matrices   n S C satisfies then           , , n ABA A B A A B S        C ,   Φ t f A SA S   for all   n A S C  , where f is an injective homomorphism on , is a complex orthogonal matrix and C S f A is the image of A under f applied entrywise.

We present the following reflexivity-like result concerning the automorphism group of the C∗-algebra B(H), H being a separable Hilbert space. Let φ : B(H) → B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then φ is an automorphism...

Let $${{\mathfrak {A}}}\, $$ and '$$ be two $$C^*$$ -algebras with identities $$I_{{{\mathfrak }$$ '}$$ , respectively, $$P_1$$ $$P_2 = I_{{{\mathfrak } - P_1$$ nontrivial projections in . In this paper, we study the characterization of multiplicative $$*$$ -Lie–Jordan-type maps, where notion these maps arise here. particular, if $${\mathcal {M}}_{{{\mathfrak is a von Neumann algebra relative $...

Let [Formula: see text] and be two alternative ∗-algebras with identities text], respectively, nontrivial symmetric idempotents in text]. In this paper, we study the characterization of multiplicative ∗-Lie-type maps. As application, get a result on text]-algebras.

Mirror principle is a general method developed in [LLY1]-[LLY4] to compute characteristic classes and characteristic numbers on moduli spaces of stable maps in terms of hypergeometric type series. The counting of the numbers of curves in Calabi-Yau manifolds from mirror symmetry corresponds to the computation of Euler numbers. This principle computes quite general Hirzebruch multiplicative clas...

We show that the notion of asymptotic lift generalizes naturally to normal positive maps φ : M → M acting on von Neumann algebras M . We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem M∞ ⊆ M , and characterize when M∞ is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of φ.

We investigate the multiplicative loops of finite semifields. We show that the group generated by the left and right multiplication maps contains the special linear group. This result solves a BCC18 problem of A. Drápal. Moreover, we study the question of whether the bigMathieu groups can occur asmultiplication groups of loops. © 2009 Elsevier Ltd. All rights reserved.