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Some summability properties of operators on a separable Banach space



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Martín Peinador, Elena (1990) Some summability properties of operators on a separable Banach space. Archiv der Mathematik, 55 (6). pp. 584-587. ISSN 0003-889X

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Official URL: http://link.springer.com/article/10.1007%2FBF01191694#



It is a well known fact that operators on a separable Hilbert space H giving norm-summability on an orthonormal basis have to be nuclear (Holub 1972) and operators giving summability on an orthonormal basis must be Hilbert-Schmidt. In former papers the author characterizes all the sequences of H that in this respect behave as orthonormal basis, and in the present paper those results are in some way, generalized to a separable Banach space.

Item Type:Article
Uncontrolled Keywords:Compact operator; nuclear operator; absolutely summable sequence; norm-summability on an orthonormal basis; Hilbert-Schmidt
Subjects:Sciences > Mathematics > Topology
ID Code:21824
Deposited On:12 Jun 2013 16:46
Last Modified:12 Dec 2018 15:13

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