TY - CHAP

T1 - Submultiplicative operators on Ck-spaces

AU - Faifman, Dmitry

AU - König, Hermann

AU - Milman, Vitali

N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - Let I⊂ ℝ be open, let k∈ N0 and T : Ck(I) →Ck(I) be bijective, pointwise continuous and submultiplicative, i.e., (Formula presented) Suppose also that T (-1) < 0 and that T and T-1 are positivity preserving. We show that there is a homeomorphism u : I → I and that there are continuous functions p,A ∈ C(I) with p > 0, A ≥ 1 such that (Formula presented). For k ∈ N, we have A = p = 1, and u is a Ck-diffeomorphismus so that Tf(u(x)) = f(x), i.e., T is multiplicative for k ∈ N. This rigidity property also holds for supermultiplicative operators.

AB - Let I⊂ ℝ be open, let k∈ N0 and T : Ck(I) →Ck(I) be bijective, pointwise continuous and submultiplicative, i.e., (Formula presented) Suppose also that T (-1) < 0 and that T and T-1 are positivity preserving. We show that there is a homeomorphism u : I → I and that there are continuous functions p,A ∈ C(I) with p > 0, A ≥ 1 such that (Formula presented). For k ∈ N, we have A = p = 1, and u is a Ck-diffeomorphismus so that Tf(u(x)) = f(x), i.e., T is multiplicative for k ∈ N. This rigidity property also holds for supermultiplicative operators.

KW - Approximate indicator

KW - Positivity preserving diffeomorphism

KW - Submultiplicative operators

UR - http://www.scopus.com/inward/record.url?scp=85044734296&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-59078-3_13

DO - 10.1007/978-3-319-59078-3_13

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AN - SCOPUS:85044734296

T3 - Operator Theory: Advances and Applications

SP - 267

EP - 279

BT - Operator Theory

PB - Springer International Publishing

ER -