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...

We investigate the class of N -determined p-compact groups and the class of p-compact groups with N -determined automorphisms. A p-compact group is said to be N -determined if it is determined up to isomorphism by the normalizer of a maximal torus. The automorphisms of a p-compact group are said to be N -determined if they are determined by their restrictions to this maximal torus normalizer.

By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and anti-automorphisms of the lattice L of all closed subspaces of E. A connection between the automorphism group of the ring of all continuous linear mappings defined on ...

For any field k and integers n ≥ 1, d ≥ 3, with (n, d) not equal to (1, 3) or (2, 4), we exhibit a smooth hypersurface X over k of degree d in Pn+1 such that X has no non-trivial automorphisms over k. For (n, d) = (2, 4), we find X such that X has no non-trivial automorphisms induced by an automorphism of the ambient Pn+1.

We consider the topological entropy of state space and quasi-state space homeomorphisms induced from C∗-algebra automorphisms. Our main result asserts that, for automorphisms of separable exact C∗-algebras, zero Voiculescu-Brown entropy implies zero topological entropy on the quasi-state space (and also more generally on the entire unit ball of the dual). As an application we obtain a simple de...

It is shown that the linear group of automorphism of Hermitian matrices which preserves the tensor product of unitary orbits is generated by natural automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. The result is then applied to show that automorphisms of the product numerical...

The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for T automorphisms is studied. Using algebraic number theory, a link is established between equality of BFgroups for different automorphisms (BF -equivalence) and an identical position in a finite lattice (L-equivalence). Important cases of equivalence of the two conditions are proved. Finally, a topolo...

in this paper, we introduce the  probabilistic normed groups. among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. we also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an algebra constant rank with center $C$ and $\sigma$ automorphism $D$, such that $\sigma|_{C}$ has finite order. The automorphisms these are canonically induced by ring the $D[t;\sigma]$ used in their construction. achieve description inner automorphisms. Results on ...

Let f : A → A be a polynomial automorphism of dynamical degree δ ≥ 2 over a number field K. (This is equivalent to say that f is a polynomial automorphism that is not triangularizable.) Then we construct canonical height functions defined on A(K) associated with f . These functions satisfy the Northcott finiteness property, and an Kvalued point on A(K) is f -periodic if and only if its height i...