Orthogonal measures for uniform algebras of finite type

In this paper we study uniform algebras of finite type. The sufficient conditions are presented for a continuous function to belong to a maximal subalgebra of the algebra C(X).Translated from Matematicheskie Zametki, Vol. 18, No. 1, pp. 109–114, July, 1975.The author expresses his gratitude to E. A. Gorin for valuable advice and discussions.     

A remark on nonlocal algebras

The construction of examples of nonlocal uniform Banach algebras (similar to the well-known example given by E. Kallin) required always considerable efforts and it could create the impression that nonlocal algebras are infrequent. It turns out that one can construct such algebras by starting practically with any uniform algebras. One gives a simple and general method for constructing nonlocal algebras, based on the use of nonlocal point derivations. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 65, pp. 172–177, 1976.     

On branching index of algebraic extension spectrum points

The paper studies the branching A-index and the topological branching index of points of the spectrum of Arens-Hoffman algebraic extension of a semisimple commutative Banach algebras A.     

Logarithms of moduli of inversible elements of a Banach algebra

The isomorphism of a separable Banach algebra of continuous functions with C(X) is deduced from the properties of the set of logarithms of moduli of invertible elements of the algebra.Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 373–377, March, 1978.     

On an Algebraic Extension of A(E)

An algebraic extension of the algebra A(E), where E is a compactum in with nonempty connected interior, leads to a Banach algebra B of functions that are holomorphic on some analytic set K^{o 2} with boundary bK and continuous up to bK. The singular points of the spectrum of B and their defects are investigated. For the case in which B is a uniform algebra, the depth of B in the algebra C(bK) is estimated. In particular, conditions under which B is maximal on bK are obtained.