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On spectrality criterion for operators on a direct sum of Hilbert spaces

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Abstract

In [1, Theorem 2.7] N. Dunford gave a necessary and sufficient condition for an operator in Up to be spectral. The purpose of this note is to furnish a direct proof for his criterion avoiding the use of his Lemma 2.5 and Theorem 2.6 of [1].

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Bibliography

  1. N. Dunford,A spectral theory for certain operators on a direct sum for Hilbert spaces, Math. Annalen162 (1966), 294–330.

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  2. W. G. Bade,Weak and strong limits of spectral operators, Pacific J. of Math.4 (1954), 393–413.

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Israel

    S. R. Foguel

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  1. S. R. Foguel
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The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.

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Foguel, S.R. On spectrality criterion for operators on a direct sum of Hilbert spaces. Israel J. Math. 3, 248–250 (1965). https://doi.org/10.1007/BF03008403

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  • DOI: https://doi.org/10.1007/BF03008403

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