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Homotonic algebras

Tom 195 / 2009

Michael Cwikel, Moshe Goldberg Studia Mathematica 195 (2009), 287-295 MSC: Primary 15A60, 16B99, 17A05, 17A15. DOI: 10.4064/sm195-3-7

Streszczenie

An algebra $\mathcal{A}$ of real- or complex-valued functions defined on a set ${\bf T}$ shall be called homotonic if $\mathcal{A}$ is closed under taking absolute values, and for all $f$ and $g$ in $\mathcal{A}$, the product $f\times g$ satisfies $|f\times g|\le|f|\times|g|$. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.

Autorzy

  • Michael CwikelDepartment of Mathematics
    Technion – Israel Institute of Technology
    Haifa 32000, Israel
    e-mail
  • Moshe GoldbergDepartment of Mathematics
    Technion – Israel Institute of Technology
    Haifa 32000, Israel
    e-mail

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