Some remarks on Toeplitz multipliers and Hankel matrices

Studia Mathematica

Volumn 175, Issue 2, 2006, Pages 175-204

  PeŁczyński, Aleksander ^a,b   Sukochev, Fyodor ^a,c  

^a Polish Academy of Sciences ^*

^b INSTITUTE OF MATHEMATICS   (Poland)

^c FLINDERS UNIVERSITY   (Australia)

Author keywords

Hankel matrices; Schur and Toeplitz Schur multipliers; Toeplitz matrices; Trace classes; Upper triangular matrices

Indexed keywords

EID: 33751401550     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm175-2-5     Document Type: Article

References (36)

1. [A] W. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208-233.
2. [Bn] G. Bennett, Schur multipliers, Duke J. Math. 44 (1977), 603-631.
3. [BP] O. Blasco and A. Pełczyński, Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces, Trans. Amer. Math. Soc. 333 (1991), 331-367.
4. p(H), Pacific J. Math. 119 (1985), 89-101.
5. [DeF] A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, Amsterdam, 1993.
6. [DoS] P. Dodds and F. Sukochev, RUC-decompositions in symmetric operator spaces, Integral Equations Operator Theory 29 (1997), 269-287.
7. [Dg] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
8. [DnSc] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1958.
9. p Spaces, Academic Press, New York, 1970.
10. [EL] P. P. B. Eggermont and Y. J. Leung, On a factorization problem for convergent sequences and on Hankel forms in bounded sequences, Proc. Amer. Math. Soc. 96 (1986), 269-274.
11. [GK] I. C. Gohberg and M. G. Kreǐa, Theory and Applications of Volterra Operators in Hilbert Spaces, Transl. Math. Monogr. 24, Amer. Math. Soc., Providence, RI, 1970.
12. [GrM] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Grundlehren Math. Wiss. 238, Springer, Berlin, 1979.
13. [HL] G. H. Hardy and J. E. Littlewood, Theorems concerning mean values of analytic or harmonic functions, Quart. J. Math. Oxford Ser. 12 (1941), 221-256.
14. [K] J.-P. Kahane, Sur les polynômes à coefficients unimodulaires, Bull. London Math. Soc. 12 (1980), 321-342.
15. [KKL] J.-P. Kahane, Y. Katznelson et K. de Leeuw, Sur les coefficients de Fourier des fonctions continues, C. R. Acad. Sci. Paris Sér. I 285 (1977), 1001-1004.
16. [KnKw] H. König and S. Kwapień, Best Khintchine type inequalities for sums of independent random variables, Positivity 5 (2001), 115-152.
17. [KwP] S. Kwapień and A. Pełczyński, On two problems of S. Mazur from the Scottish Book, lecture at the Colloquium dedicated to the memory of Stanisław Mazur, Warsaw Univ., 1985 (unpublished).
18. [L] J. E. Littlewood, On bounded bilinear forms in an infinite number of variables, Quart. J. Math. 1 (1930), 164-174.
19. [Lu] F. Lust-Piquard, On the coefficient problem: a version of the Kahane-Katznel-son-de Leeuw theorem for spaces of matrices, 3. Funct. Anal. 149 (1997), 352-376.
20. [M] B. Maurey, Tout opérateur d'une C*-algèbre dans un espace de cotype 2 se factorise par un Hilbert, d'après G. Pisier, Séminaire sur la géométrie des espaces de Banach, 1975-1976, École Polytechnique, exp. XXI.
21. [MiP] B. S. Mityagin and A. Pełczyński, Nuclear operators and approximative dimension, in: Proc ICM Moscow, 1966, 366-372.
22. [N] F. Nazarov, The Bang solution to the coefficient problem, Algebra i Analiz 9 (1987), 272-287 (in Russian).
23. [O] W. Orlicz, Über unbedingte Konvergenz in Funktionenräumen, Studia Math. 4 (1934), 33-37.
24. [Ov] V. I. Ovchinnikov, Noncommutative BMO spaces, coherent nuclearity, and bounded extensions of matrices, Dokl. Akad. Nauk 363 (1998), 17-19 (Russian).
25. [Pa 1] R. E. A. C. Paley, On the lacunary coefficients of power series, Ann. of Math. 34 (1936), 615-616.
26. [Pa 2] _, A note on power series, J. London Math. Soc. 7 (1932), 122-130.
27. [Pe] V. V. Peller, Hankel Operators and Their Applications, Springer Monogr. Math., Springer, Berlin, 2003.
28. [Pi 1] G. Pisier, Grothendieck's theorem for non-commutative C*-algebras, with an appendix on Grothendieck's constant, J. Funct. Anal. 29 (1978), 397-415.
29. p-spaces and non-commutative generalizations. I, Pacific J. Math. 155 (1992), 341-368.
30. [Pi 3] _, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts Math. 94, Cambridge Univ. Press, Cambridge, 1989.
31. p-spaces, in: Handbook of the Geometry of Banach Spaces, Vol. II, Elsevier, Amsterdam, 2003, 1459-1517.
32. [Scb] The Scottish Book, R. D. Mauldin (ed.), Birkhäuser, Boston, MA, 1979.
33. [Sh] A. L. Shields, An analogue of a Hardy-Littlewood-Fejér inequality for upper triangular trace class operators, Math. Z. 182 (1983), 473-484.
34. 1 multiplier theorem, Ark. Mat. 19 (1981), 265-270.
35. [SzW] S. J. Szarek and T. Wolniewicz, A proof of Fefferman's theorem on multipliers, Inst. Math., Polish Acad. Sci., Preprint No. 209 (1980).
36. [Z] A. Zygmund, Trigonometric Series, Vol. I, 2nd ed., Cambridge Univ. Press, Cambridge, 1959.