2022
DOI: 10.1007/s13398-022-01284-8
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On diagonal operators between the sequence (LF)-spaces $$l_p({\mathcal {V}})$$

Abstract: Diagonal (multiplication) operators acting between a particular class of countable inductive spectra of Fréchet sequence spaces, called sequence (LF)-spaces, are investigated. We prove results concerning boundedness, compactness, power boundedness, and mean ergodicity. Furthermore, we determine when a diagonal operator is Montel and reflexive. We analyze the spectra in terms of the system of weights defining the spaces.

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Cited by 2 publications
(3 citation statements)
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“…The characterization of the continuity of operators between (LF)‐spaces is well‐known and due to Grothendieck. The characterization of boundedness as well as the compactness of operators acting between (LF)‐spaces has been given in [17] as follows (see also [7, Proposition 5], where the (LB)‐case is considered). We include also the weakly compact case.…”
Section: Definitions and General Results On (Lf)‐ And (Plb)‐spacesmentioning
confidence: 99%
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“…The characterization of the continuity of operators between (LF)‐spaces is well‐known and due to Grothendieck. The characterization of boundedness as well as the compactness of operators acting between (LF)‐spaces has been given in [17] as follows (see also [7, Proposition 5], where the (LB)‐case is considered). We include also the weakly compact case.…”
Section: Definitions and General Results On (Lf)‐ And (Plb)‐spacesmentioning
confidence: 99%
“…We refer the reader to [17] for analogous results on diagonal (multiplication) operators acting on the sequence (LF)‐space lp(V)$l_p(V)$, with 1p$1\le p\le \infty$ or p=0$p=0$.…”
Section: Examplesmentioning
confidence: 99%
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