Some summability properties of operators on a separable Banach space
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1990
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Birkhäuser Verlag
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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).
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.