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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 2, Pages 310–314 (Mi smj2198)  
This article is cited in 1 scientific paper (total in 1 paper)

On some algebra of continuous linear operators

V. B. Korotkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
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Abstract: We present a criterion for an operator on $L_p$ to belong to the set $I_p$ of all sums of integral operators on $L_p$ and multiplication operators by functions in $L_\infty$. We describe the closure of $I_p$ in the operator norm. We prove that the set $L_{p,1}$ of all sums of multiplication operators and operators on $L_p$ mapping the unit ball of $L_p$ into compact subsets of $L_1$ is a Banach algebra.
Keywords: integral operator, multiplication operator, integral operator of the third kind, almost compact operator, $\langle p,1\rangle$-compact operator, Banach algebra, essential spectrum.
Received: 16.04.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 2, Pages 244–247
DOI: https://doi.org/10.1134/S0037446611020078
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
Citation: V. B. Korotkov, “On some algebra of continuous linear operators”, Sibirsk. Mat. Zh., 52:2 (2011), 310–314; Siberian Math. J., 52:2 (2011), 244–247
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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