Approximation of multipliers

Gaudry, Garth I.; Inglis, Ian R.

doi:10.1090/S0002-9939-1974-0340970-8

Approximation of multipliers
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by Garth I. Gaudry and Ian R. Inglis PDF

Proc. Amer. Math. Soc. 44 (1974), 381-384 Request permission

Abstract:

We note some necessary and sufficient conditions concerning norm approximation of Fourier multipliers, and give an example to show that ${M_q}(Z)$, the space of Fourier multipliers of type $(q,q)$, is not norm dense in ${M_p}(Z)$ when $1 \leqq q < p \leqq 2$. An extension of this example to more general groups is indicated.

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