Monotone substochastic operators and a new Calderón couple

• Autorzy: Karol Leśnik
• Języki publikacji: EN

Abstrakty

EN

An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that b ⪯ a if and only if there is a doubly stochastic matrix A such that b = Aa. We prove that under monotonicity assumptions on the vectors a and b the matrix A may be chosen monotone. This result is then applied to show that $(\widetilde{L^{p}},L^{∞})$ is a Calderón couple for 1 ≤ p < ∞, where $\widetilde{L^{p}}$ is the Köthe dual of the Cesàro space $Ces_{p'}$ (or equivalently the down space $L^{p'}_{↓}$). In particular, $(\widetilde{L¹},L^{∞})$ is a Calderón couple, which gives a positive answer to a question of Sinnamon [Si06] and complements the result of Mastyło and Sinnamon [MS07] that $(L^{∞}_{↓},L¹)$ is a Calderón couple.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B70: Interpolation between normed linear spaces
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 1
• Strony: 21-39

Daty

wydano

2015

Twórcy

autor

Karol Leśnik

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland

Identyfikatory

DOI

10.4064/sm227-1-2