Some Remarks on the Spectral Properties of Toeplitz Operators

Aiena, Pietro; Triolo, Salvatore

doi:10.1007/s00009-019-1397-8

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2020

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Cited by 3 publications

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“…Since R j−n is upper semi-Fredholm, the SVEP at 0 implies that H 0 (R j−n ) is finite-dimensional (see [8], Theorem 3.18). Then, X R j−n ({λ} ∪ {0}) is closed.…”

Section: Theoremmentioning

confidence: 99%

Local Spectral Theory for R and S Satisfying RnSRn = Rj

Triolo

2020

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In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j≥n≥0. We also continue to study the relationship between the local spectral properties of an operator R and the local spectral properties of S. Thus, we investigate the transmission of some local spectral properties from R to S and we illustrate our results with an example. The theory is exemplified in some cases.

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“…Since R j−n is upper semi-Fredholm, the SVEP at 0 implies that H 0 (R j−n ) is finite-dimensional (see [8], Theorem 3.18). Then, X R j−n ({λ} ∪ {0}) is closed.…”

Section: Theoremmentioning

confidence: 99%