Abstract
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.
Highlights
In a preceding paper [1] we proved a sewing lemma which was a key result for the study of Holder continuous functions
In the second section we prove the non-commutative version. This last result has interesting applications : an extension of the so-called integral product, a simple case of the semigroup Trotter type formula, and a sharpening of the Lyons theorem about multiplicative functionals [3,4,5]
In the case where A is a complex Banach algebra, the proof of the multiplicative sewing lemma yields a sequence of holomorphic functions which converges uniformly with respect to λ in every compact set of C|
Summary
In a preceding paper [1] we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma. In the first section we recall the commutative version, and give some applications (Young integral and stochastic integral). In the second section we prove the non-commutative version. This last result has interesting applications : an extension of the so-called integral product, a simple case of the semigroup Trotter type formula, and a sharpening of the Lyons theorem about multiplicative functionals [3,4,5]. Note that we replaced the Holder modulus of continuity tα by a more general modulus V (t).
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