Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition ...

Let R be a semiprime ring and let F, f : R → R be (not necessarily additive) maps satisfying F (xy) = F (x)y + xf(y) for all x, y ∈ R. Suppose that there are integers m and n such that F (uv) = mF (u)F (v) + nF (v)F (u) for all u, v in some nonzero ideal I of R. Under some mild assumptions on R, we prove that there exists c ∈ C(I) such that c = (m + n)c2, nc[I, I] = 0 and F (x) = cx for all x ∈...

Let A and B be uniform algebras on first-countable, compact Hausdorff spaces X and Y , respectively. For f ∈ A, the peripheral spectrum of f , denoted by σπ(f) = {λ ∈ σ(f) : |λ| = ‖f‖}, is the set of spectral values of maximum modulus. A map T : A → B is weakly peripherally multiplicative if σπ(T (f)T (g)) ∩ σπ(fg) 6= ∅ for all f, g ∈ A. We show that if T is a surjective, weakly peripherally mu...

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 $...

This work is concerned with consensus problem of multi-agent systems with additive and multiplicative measurement noises. By developing general stochastic stability lemmas for nonautonomous stochastic differential equations, stochastic weak and strong consensus conditions are investigated under fixed and time-varying topologies, respectively. For the case with fixed topologies and additive nois...

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.