ACTA issues

A norm estimate for holomorphic operator functions in an ordered Banach space

Michael Gil'

Acta Sci. Math. (Szeged) 80:1-2(2014), 141-148

Abstract. The paper deals with holomorphic functions of a bounded operator $A$ acting in a Banach complex lattice. A norm estimate for the considered operator valued functions is derived. Applications of the obtained bound to functions of integral operators, partial integral operators, infinite matrices and differential equations are also discussed.

DOI: 10.14232/actasm-012-052-x

AMS Subject Classification (1991): 46B42, 47A56, 47A60, 47G10, 35A23

Keyword(s): Banach lattice, operator functions, integral operators, infinite matrices, partial integral operator, Barbashin equation

Received July 13, 2012. (Registered under 52/2012.)