Concentration Week on Ideals and Algebras of Operators on Banach Spaces

Description

This event is intended to bring together researchers interested in the various aspects of spaces of operators in Banach spaces. Particular emphasis is given to the rich theory induced by quotients over classical ideals as well as by the plenitude of different ideals.

Although in the separable Hilbert space setting, the algebra of bounded linear operators only contains one non-trivial closed ideal, the compact operators, in other separable spaces, this is often not the case. Of particular importance in the general theory are the ideals of approximable operators, of compact operators, and of strictly singular operators. These classes are directly connected to the approximation property,  Fredholm operator theory, the unconditional basis problem, and K-theory. It is not surprising that this wealth has, since the 1980s, promoted a search for new closed ideals in classical and non-classical spaces. This was fueled by the then-recent discovery of uncountably many complemented subspaces in reflexive Lp-spaces. Further important leaps were made in the 2000s, 2010s, and 2020s, culminating in the construction of a continuum of closed ideals in L1 and 2c closed ideals in reflexive Lp spaces, as well as in other important Banach spaces.

The purpose of the Concentration Week on Ideals and Algebras of Operators on Banach Spaces is to showcase and bring together cutting-edge technologies in constructing and studying ideals in the algebras of bounded linear operators on classical and non-classical spaces, draw parallels to the study of C* and operator algebras, and set the tone for future research directions in the field.

 Organizers

• William B. Johnson (Texas A&M University)

• N. Christopher Phillips (University of Oregon)

• Piotr Koszmider (Mathematical Institute of the Polish of Academy of Sciences)

• Pavlos Motakis (York University)