Extreme points and isometries of φ-nuclear operators in Hilbert spaces

Abstract

A modulus function φ is a continuous strictly increasing subadditive real valued function φ: [0, ∞) → [0, ∞) for which φ(0) = 0. The object of this paper is to define φ-nuclear operators in Banach spaces. The basic properties of these operators are studied. In particular it is proved that φ-nuclear operators are stable under injective tensor product. In case of Hilbert spaces, the extreme points of the unit ball and the isometrics of such class of operators are characterized.