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Some criteria for nuclearity

Published online by Cambridge University Press:  24 October 2008

M. A. Sofi
M. A. Sofi
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202001, India
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Extract

For a given locally convex space, it is always of interest to find conditions for its nuclearity. Well known results of this kind – by now already familiar – involve the use of tensor products, diametral dimension, bilinear forms, generalized sequence spaces and a host of other devices for the characterization of nuclear spaces (see [9]). However, it turns out, these nuclearity criteria are amenable to a particularly simple formulation in the setting of certain sequence spaces; an elegant example is provided by the so-called Grothendieck–Pietsch (GP, for short) criterion for nuclearity of a sequence space (in its normal topology) in terms of the summability of certain numerical sequences.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 151 - 159
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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