Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović; Dragoljub Kečkić

Studia Mathematica, Tome 173 (2006), p. 149-166 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider elementary operators $x \mapsto \sum_{j = 1}^{n} a_{j} x b_{j}$ , 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. $a_{j} = a_{j}^{'} + i a_{j}^{''}$ ( $b_{j} = b_{j}^{'} + i b_{j}^{''}$ ), where all $a_{j}^{'}$ and $a_{j}^{''}$ ( $b_{j}^{'}$ and $b_{j}^{''}$ ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of $C_{c p t}^{\infty}$ functions on $ℝ^{2 n}$ .

Publié le : 2006-01-01

Zbl 1094.47038

EUDML-ID : urn:eudml:doc:284423

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     author = {Milo\v s Arsenovi\'c and Dragoljub Ke\v cki\'c},
     title = {Elementary operators on Banach algebras and Fourier transform},
     journal = {Studia Mathematica},
     volume = {173},
     year = {2006},
     pages = {149-166},
     zbl = {1094.47038},
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Miloš Arsenović; Dragoljub Kečkić. Elementary operators on Banach algebras and Fourier transform. Studia Mathematica, Tome 173 (2006) pp. 149-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-3/