A+ CATEGORY SCIENTIFIC UNIT

Elementary operators on Banach algebras and Fourier transform

Volume 173 / 2006

Miloš Arsenović, Dragoljub Kečkić Studia Mathematica 173 (2006), 149-166 MSC: 47B48, 47B47, 42B10. DOI: 10.4064/sm173-2-3

Abstract

We consider elementary operators $x\mapsto\sum_{j=1}^na_jxb_j$, acting on a unital Banach algebra, where $a_j$ and $b_j$ are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede–Putnam theorem for an elementary operator with strongly commuting families $\{a_j\}$ and $\{b_j\}$, i.e. $a_j=a_j'+ia_j''$ ($b_j=b_j'+ib_j''$), where all $a_j'$ and $a_j''$ ($b_j'$ and $b_j''$) commute. The main tool is an $L^1$ estimate of the Fourier transform of a certain class of $C_{\rm cpt}^\infty$ functions on $\mathbb R^{2n}$.

Authors

  • Miloš ArsenovićMatematički Fakultet
    Univerzitet u Beogradu
    Studentski trg 16–18
    11000 Beograd, Serbia and Montenegro
    e-mail
  • Dragoljub KečkićMatematički Fakultet
    Univerzitet u Beogradu
    Studentski trg 16–18
    11000 Beograd, Serbia and Montenegro
    e-mail

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