On the relationship between \(\gamma_ p\)-Radonifying operators and other operator ideals in Banach spaces of stable type p (Q1118141)

Let E be a Banach space, p a real number with \(1<p<2\), and \((\Omega,\Sigma,\mu)\) a \(\sigma\)-finite measure space. A bounded operator T from \(L_ p(\mu)\) into E is said to be \(\gamma_ p\)-Radonifying if \(\exp (-\| T'x'\|^ p)\) is the characteristic function of a Radon measure on E. The authors study the relationship between such operators and various operator ideals. For example, the condition ``E is of stable type p and isomorphic to a subspace of a quotient of some \(L_ p\) space'' is equivalent to the condition ``an operator T is \(\gamma_ p\)- Radonifying iff its dual \(T'\) is p-integral''.