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Currently displaying 1 – 2 of 2

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Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović; Dragoljub Kečkić — 2006

Studia Mathematica

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...

A counterexample on a theorem by Khojasteh, Goodarzi, and Razani.

Arandelović, Ivan D.; Kečkić, Dragoljub J. — 2010

Fixed Point Theory and Applications [electronic only]

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