Derivations preserving quasinilpotent elements

Dependent Elements of Derivations on Semiprime Rings

Microspectral Analysis of Quasinilpotent Operators

We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(Q) = {0}) in a Banach space. When such Q is not compact, normal, or nilpotent, the classical spectral theory gives little information, and a somewhat deeper structure can be recovered from microspectral sets in C. Such sets describe, e.g., semigroup generation, resolvent properties, power boundedness as ...

Linear maps on von-Neumann algebras behaving like anti-derivations at orthogonal elements

This article has no abstract.

Hyperinvariant subspaces and quasinilpotent operators

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

Some Quasinilpotent Generators of the Hyperfinite Ii1 Factor

Abstract. For each sequence {cn}n in l1(N) we define an operator A in the hyperfinite II1-factor R. We prove that these operators are quasinilpotent and they generate the whole hyperfinite II1-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra and we provide enough evidence to suggest that these operators are interesting for the hyperin...