On the Structure of Conditionally Positive Definite Algebraic Operators

Abstract

AbstractRecently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its origins go back to the harmonic analysis on $$*$$ ∗ -semigroups, namely to the concept of conditional positive definiteness. Our main aim here is to give a complete description of algebraic conditionally positive definite operators on inner product spaces; we do not assume that the operators under consideration are bounded.