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Journal of Soviet Mathematics

, Volume 31, Issue 1, pp 2709–2712 | Cite as

Hankel-Schur multipliers and multipliers of the space H1

  • V. V. Peller
Article

Abstract

In this paper there is given a sufficient condition for a Hankel matrix γF to belong to the space of Schur multipliers of all bounded operators inœ2 (or, what is the same, to the tensor algebra V2). It is shown that ifw is a nonnegative function on T, such that
is a sequence of integers,
{Fi}j1 is a sequence of polynomials,
) and
, then λF∃V2. It follows from this that under these conditions F is a multiplier of the space H1, i.e.,
.

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Literature cited

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    G. Bennett, “Schur multipliers,” Duke Math. J.,44, 603–639 (1977).CrossRefGoogle Scholar
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    V. V. Peller, “Estimates of functions of power bounded operators on Hilbert spaces,” J. Oper. Theory,7, No. 2, 341–372 (1982).Google Scholar
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    M. Sh. Birman and M. Z. Solomyak, “Dual operator Stieltjes integrals. III. Passage to the limit under the integral sign,” Probl. Mat. Fiz.,6, 27–53 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • V. V. Peller

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