Journal of Operator Theory
Volume 91, Issue 2, Spring 2024 pp. 323-333.
Operateurs hypofermes
Authors:
Jacques Dixmier
Author institution: 11bis rue du Val de Grace, Paris 75005, France
Summary: Range spaces of bounded linear operators between Hilbert spaces, as well as linear operators between Hilbert spaces, whose graph is a bounded linear range of some Hilbert space, were systematically studied in an early paper. Here extensions of the above topics to the framework of general Banach spaces are discussed. A hypoclosed linear subspace of a Banach space is the range space of a bounded linear operator defined on some Banach space, while a hypoclosed linear operator is a linear operator between Banach spaces, whose graph is hypoclosed. Characterizations, permanence properties, pathologies are presented, and several significant differences to the Hilbert space case are emphasized.
DOI: http://dx.doi.org/10.7900/jot.2023nov13.2451
Keywords: sous-espaces hypofermes, presentation d’un sous-espace hypoferme, homomorphismes hypofermes
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