Trivial endomorphisms of the Calkin algebra

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Asymptotic homomorphisms into the Calkin algebra ∗

Let A be a separable C∗-algebra and let B be a stable C∗-algebra with a strictly positive element. We consider the (semi)group Ext(A,B) (resp. Ext(A,B)) of homotopy classes of asymptotic (resp. of genuine) homomorphisms from A to the corona algebra M(B)/B and the natural map i : Ext(A,B) −→ Ext(A,B). We show that if A is a suspension then Ext(A,B) coincides with E-theory of Connes and Higson an...

Ruled Surfaces with Non-trivial Surjective Endomorphisms

Let X be a non-singular ruled surface over an algebraically closed field of characteristic zero. There is a non-trivial surjective endomorphism f : X → X if and only if X is (1) a toric surface, (2) a relatively minimal elliptic ruled surface, or (3) a relatively minimal ruled surface of irregularity greater than one which turns to be the product of P and the base curve after a finite étale bas...

compact endomorphisms of certain subalgebras of the disk algebra

Masas in the Calkin Algebra without the Continuum Hypothesis

Methods for constructing masas in the Calkin algebra without assuming the Continuum Hypothesis are developed.