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Integrable factors in compact Schur multipliers


Author: Mats Erik Andersson
Journal: Proc. Amer. Math. Soc. 133 (2005), 1469-1473
MSC (2000): Primary 47A68; Secondary 47B07, 42A38, 43A46
DOI: https://doi.org/10.1090/S0002-9939-04-07670-1
Published electronically: December 6, 2004
MathSciNet review: 2111947
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Abstract: It is shown that a Schur multiplier is compact if and only if it is the Schur product of two multipliers, one of which is a Hankel-Schur multiplier generated by an integrable function. This is illuminated by factoring exotic, singular measures and is brought into relation with Paley set-based multipliers.


References [Enhancements On Off] (What's this?)

  • [A] M.E. Andersson, Two special applications of Riesz products, Fourier analysis and related topics, vol. 56, Banach Center Publications, Warszawa, 2002, pp. 13-29. MR 1971560 (2004b:42019)
  • [Be] G. Bennett, Schur multipliers, Duke Math. J. 44 (1977), 603-639. MR 0493490 (58:12490)
  • [Bo] M. Bozejko, Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space, Colloq. Math. 51 (1987), 35-42. MR 0891273 (88i:47011)
  • [F] J.J.F. Fournier, Extensions of a Fourier multiplier theorem of Paley, Pacific J. Math. 30 (1969), 415-431. MR 0257651 (41:2301)
  • [H] M. Hladnik, Compact Schur multipliers, Proc. of Amer. Math. Soc. 128 (9) (2000), 2585-2591. MR 1766604 (2002a:46081)
  • [HR] E. Hewitt and K. Ross, Abstract harmonic analysis II, Springer Verlag, Berlin-Heidelberg-New York, 1970. MR 0262773 (41:7378)
  • [K] I. Klemes, Idempotent multipliers of $H^{1}(\mathbb{T} )$, Canad. J. Math. 39 (5) (1987), 1223-1234. MR 0918595 (88k:42007)
  • [R] W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (2) (1960), 203-227. MR 0116177 (22:6972)

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Additional Information

Mats Erik Andersson
Affiliation: Bellmansgatan 118, SE-754 26 Uppsala, Sweden
Email: mats@math.uu.se

DOI: https://doi.org/10.1090/S0002-9939-04-07670-1
Keywords: Riesz products, Paley sets, Littlewood multiplier, compact operator, Hardy space multiplier
Received by editor(s): October 8, 2003
Received by editor(s) in revised form: February 1, 2004
Published electronically: December 6, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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