Publication:
Some summability properties of operators on a separable Banach space

Loading...
Thumbnail Image
Full text at PDC
Publication Date
1990-12-03
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Birkhäuser Verlag
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
J.Diestel, Sequences and Series in Banach spaces. Berlin-Heidelberg-New York 1984. J. R. Holub, Characterization of nuclear operators in Hilbert space. Rev. Roumaine Math. Pures Appl. (5) 16, 687–690 (1971). H. König, Personal Communication. 1985. E. Martín-Peinador, On the set of bounded linear operators transforming a sequence of a Hilbert space into an absolutely summable one. Colloq. Mat. Soc. János Bolyai 23, 829–837 (1978). E. Martín-Peinador, The weak summability dominion of a sequenceS of a Hilbert space in relation with the set of bounded linear operators. Ann. Inst. Mat. Univ. Nac. Aut. de Mexico. (2) 21, 149–162 (1981).
Collections