Operators on Banach Spaces

Areas of research interest of Niels Laustsen and András Zsák.

Banach space theory originates from Banach's seminal monograph, first published in 1932. Banach's work was primarily motivated by vector spaces of functions, but many other interesting classes of Banach spaces exist, and the field is very rich in examples.

The focus of the work at Lancaster is to investigate a given Banach space E through the Banach algebra B(E) of bounded, linear operators acting on it. Often problems are motivated by results about operator algebras (which correspond to the case of operators acting on the `nicest possible' Banach space, that is, Hilbert space). The research relies on results and methods from Banach space theory, operator theory, Banach algebras, and ring theory.

Questions studied include:

• the closed ideals and the maximal ideals in B(E);
• the existence of traces and of involutions on B(E);
• the K-theory of B(E).

References

• N. Laustsen, T. Schlumprecht and A. Zsak, The lattice of closed ideals in the Banach algebra of operators on a certain dual Banach space, JOT