Uniform \(B(H)\) algebras (Q1842702)

The concept of a noncommutative uniform algebra was first introduced by \textit{D. C. Taylor} in [J. Funct. Anal. 10, No. 2, 159-190 (1972; Zbl 0245.46083)]. As a continuation of studies undertaken in [\textit{V. A. Arzumanyan} and \textit{S. A. Grigoryan}, ibid. 21, No. 1, 63-79 (1986; Zbl 0614.46050) and ibid. 23, No. 5, 422-438 (1988; Zbl 0713.46035)], we investigate noncommutative uniform algebras with a constant fiber that coincide with complete algebras of linear bounded operators on a certain Hilbert space.