Showing papers in "Ukrainian Mathematical Journal in 1985"

Description of the isomorphisms of spaces of holomorphic functions that commute with powers of a multiplication operator

Abstract: Let G be an arbitrary domain in the complex plane. We denote by H(G) the space of functions holomorphic in G endowed with the topology of compact convergence [I]; L(H) is the algebra of all linear operators in H(G), Q~ is the operator of multiplication by the function ~ E H (O) defined by the rule (Q~f) (z) ----~ (z) [ (z), [C H (O); in particular, Q = Qz designates the operator of multiplication by the independent variable z (for the fundamental role played by the operator Qz in spaces of holomorphic functions and in the theory of linear operators see [2]).

A property of the boundary spectrum of nonnegative operators

Abstract: We consider the n-dimensional real space R n, n > 3, provided with a closed solid cone K and thus being a Kantorovich space ("K-space"). Let A be a nonnegative linear operator: A ~0r c K. The multiplication of A by a positive constant does not lead out from the set of nonnegative linear operators; therefore, for the investigation of the character of the spectrum it is sufficient to restrict ourselves to the class of nonnegative operators with spectral radius equal to unity. Everywhere in the sequel, by the term "nonnegative operator" we shall mean a nonnegative linear operator with spectral radius equal to unity.