All automorphisms of all Calkin algebras

All Automorphisms of the Calkin Algebra Are Inner

We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips–Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 problem of Brown–Douglas–Fillmore. We also give a simpler and self-contained proof of the Phillips–Weaver result. ...

Some Calkin algebras have outer automorphisms

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

Automorphisms of the Semigroup of All Endomorphisms of Free Algebras

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups, modules, Lie algebras and some others (see references). All these researches were inspired by the questions prof. B. Plotkin set in connection with so calle...

All Irrational Extended Rotation Algebras Are Af Algebras

Let θ ∈ [0, 1] be any irrational number. It is shown that the extended rotation algebra Bθ introduced in [8] is always an AF algebra.

Automorphisms of Operator Algebras