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.
An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.