Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .
The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.
We give a simple complex-variable proof of an old result of Zemánek and Le Page on the radical of a Banach algebra. Incidentally, the argument also proves a recent result of Harris and Kadison.
For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.
We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.
We present an example of an algebra that is generated by elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.
We construct an example as announced in the title. We also indicate all right, left and two-sided ideals in this example.
For Banach Jordan algebras and pairs the spectrum is proved to be related to the spectrum in a Banach algebra. Consequently, it is an analytic multifunction, upper semicontinuous with a dense G delta-set of points of continuity, and the scarcity theorem holds.
Se è un'applicazione olomorfa di un domìnio di in un'algebra topologica che gode di certe proprietà, si dimostra che la multifunzione «spettro» è analitica secondo Oka.