@article{f080f4c479524a1eaa208495ef438f39,

title = "Submultiplicative functions and operator inequalities",

abstract = "Let T : C1(ℝ) → C(ℝ) be an operator satisfying the {"}chain rule inequality{"} T(f ○ g) ≤ (Tf) ○ g · Tg; f; g ∈ C1(ℝ): Imposing a weak continuity and a non-degeneracy condition on T, we determine the form of all maps T satisfying this inequality together with T(-Id)(0) < 0. They have the form (Formula presented)., with p > 0, H ∈ C(ℝ), A ≥ 1. For A = 1, these are just the solutions of the chain rule operator equation. To prove this, we characterize the submultiplicative, measurable functions K on R which are continuous at 0 and 1 and satisfy K(-1) < 0 < K(1). Any such map K has the form (formula presented)., with A ≥ 1 and p > 0. Corresponding statements hold in the supermultiplicative case with 0 < A ≤ 1.",

keywords = "Chain rule, Operator inequalities, Submultiplicative functions",

author = "Hermann K{\"o}nig and Vitali Milman",

note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2014",

year = "2014",

doi = "10.4064/sm223-3-3",

language = "אנגלית",

volume = "223",

pages = "217--231",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Instytut Matematyczny",

number = "3",

}