On the geometry of the set of square roots of elements in \(C^*\)- algebras
In the last years, a long series of papers dealing with problems from differential geometry in the context of Banach and \(C^*\)-algebras, has appeared. Thus, Gramsch studied the set of relatively regular operators, Martin studied the space of projective representations of a compact group in a \(C^*\)-algebra, Corach, Porta and Recht studied the set of idempotent elements in a \(C^*\)-algebra, the set of partitions of the identity in a Banach algebra, the set of selfadjoint invertible elements in a \(C^*\)-algebra and the set of positive invertible elements in a \(C^*\)-algebra; Andruchow and Stojanoff considered the differential structure of nilpotent operators on a Hilbert space, the geometry of unitary orbits in \(C^*\)-algebras, and in a joint work with Recht, the geometry of the space of spectral measures with values in a von Neumann algebra. In this paper we study the geometric structure of two spaces related to the set of idempotents and the set of selfadjoint invertible elements in a \(C^*\)-algebra.
projective representations of a compact group
partitions of the identity in a Banach algebra
selfadjoint invertible elements in a \(C^*\)-algebra
geometry of unitary orbits in \(C^*\)-algebras
set of selfadjoint invertible elements in a \(C^*\)-algebra
scientific article; zbMATH DE number 638262
scientific article