Schur multiplier characterization of a class of infinite matrices

A. Marcoci; L. Marcoci; L. E. Persson; N. Popa

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 1, page 183-193
  • ISSN: 0011-4642

Abstract

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Let B w ( ℓ p ) denote the space of infinite matrices A for which A ( x ) ∈ ℓ p for all x = { x k } k = 1 ∞ ∈ ℓ p with | x k | ↘ 0 . We characterize the upper triangular positive matrices from B w ( ℓ p ) , 1 < p < ∞ , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

How to cite

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Marcoci, A., et al. "Schur multiplier characterization of a class of infinite matrices." Czechoslovak Mathematical Journal 60.1 (2010): 183-193. <http://eudml.org/doc/38000>.

@article{Marcoci2010,
abstract = {Let $B_w(\ell ^p)$ denote the space of infinite matrices $A$ for which $A(x)\in \ell ^p$ for all $x=\lbrace x_k\rbrace _\{k=1\}^\infty \in \ell ^p$ with $|x_k|\searrow 0$. We characterize the upper triangular positive matrices from $B_w(\ell ^p)$, $1<p<\infty $, by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.},
author = {Marcoci, A., Marcoci, L., Persson, L. E., Popa, N.},
journal = {Czechoslovak Mathematical Journal},
keywords = {infinite matrices; Schur multipliers; discrete Sawyer duality principle; Bennett factorization; Wiener algebra and Hardy type inequalities; infinite matrix; Schur multiplier; discrete Sawyer duality principle; Bennett factorization; Wiener algebra; Hardy type inequality; upper triangular positive matrices},
language = {eng},
number = {1},
pages = {183-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Schur multiplier characterization of a class of infinite matrices},
url = {http://eudml.org/doc/38000},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Marcoci, A.
AU - Marcoci, L.
AU - Persson, L. E.
AU - Popa, N.
TI - Schur multiplier characterization of a class of infinite matrices
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 183
EP - 193
AB - Let $B_w(\ell ^p)$ denote the space of infinite matrices $A$ for which $A(x)\in \ell ^p$ for all $x=\lbrace x_k\rbrace _{k=1}^\infty \in \ell ^p$ with $|x_k|\searrow 0$. We characterize the upper triangular positive matrices from $B_w(\ell ^p)$, $1<p<\infty $, by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.
LA - eng
KW - infinite matrices; Schur multipliers; discrete Sawyer duality principle; Bennett factorization; Wiener algebra and Hardy type inequalities; infinite matrix; Schur multiplier; discrete Sawyer duality principle; Bennett factorization; Wiener algebra; Hardy type inequality; upper triangular positive matrices
UR - http://eudml.org/doc/38000
ER -

References

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  1. Bennett, G., Factorizing the Classical Inequalities, Memoirs of the American Mathematical Society, Number 576 (1996). (1996) Zbl0857.26009MR1317938
  2. Bennett, G., Schur multipliers, Duke Math. J. 44 (1977), 603-639. (1977) Zbl0389.47015MR0493490
  3. Barza, S., Kravvaritis, D., Popa, N., 10.1155/2005/376150, J. Funct. Spaces Appl. 3 (2005), 239-249. (2005) Zbl1093.42002MR2163625DOI10.1155/2005/376150
  4. Badea, C., Paulsen, V., 10.1512/iumj.2001.50.2121, Indiana Univ. Math. J. 50 (2001), 1509-1522. (2001) Zbl1031.47019MR1888651DOI10.1512/iumj.2001.50.2121
  5. Barza, S., Persson, L. E., Popa, N., 10.1002/mana.200310100, Math. Nach. 260 (2003), 14-20. (2003) Zbl1043.15020MR2017699DOI10.1002/mana.200310100
  6. Barza, S., Lie, V. D., Popa, N., 10.1007/BF02384779, Ark. Mat. 43 (2005), 251-269. (2005) MR2173951DOI10.1007/BF02384779
  7. Carro, M. J., Soria, J., 10.1006/jfan.1993.1042, J. Funct. Anal. 112 (1993), 480-494. (1993) Zbl0784.46022MR1213148DOI10.1006/jfan.1993.1042
  8. Carro, M. J., Raposo, J. A., Soria, J., Recent Developments in the Theory of Lorentz Spaces and Weighted Inequalities, Memoirs of the American Mathematical Society, Number 877 (2007). (2007) Zbl1126.42005MR2308059
  9. Jagers, A. A., A note on Cesaro sequence spaces, Nieuw Arch. voor Wiskunde 3 (1974), 113-124. (1974) Zbl0286.46017MR0348444
  10. Kufner, A., Persson, L. E., Weighted Inequalities of Hardy Type, World Scientific Publishing Co., Singapore-New Jersey-London-Hong Kong (2003). (2003) Zbl1065.26018MR1982932
  11. Kufner, A., Maligranda, L., Persson, L. E., The Hardy Inequality, About its History and Some Related Results, Vydavatelsky Servis Publishing House, Pilsen (2007). (2007) MR2351524
  12. Kwapien, S., Pelczynski, A., 10.4064/sm-34-1-43-67, Studia Math. 34 (1970), 43-68. (1970) Zbl0189.43505MR0270118DOI10.4064/sm-34-1-43-67
  13. Marcoci, A., Marcoci, L., 10.1155/2007/949161, J. Funct. Spaces Appl. 5 (2007), 151-164. (2007) MR2319600DOI10.1155/2007/949161
  14. Paulsen, V., Completely Bounded Maps and Operator Algebras, Cambridge studies in advanced mathematics 78, Cambridge University Press (2002). (2002) Zbl1029.47003MR1976867
  15. Pommerenke, Chr., Univalent Functions, Hubert, Gottingen (1975). (1975) Zbl0298.30014MR0507768
  16. Sawyer, E., 10.4064/sm-96-2-145-158, Studia Math. 96 (1990), 145-158. (1990) Zbl0705.42014MR1052631DOI10.4064/sm-96-2-145-158
  17. Schur, J., 10.1515/crll.1911.140.1, J. Reine Angew. Math. 140 (1911), 1-28 2.0367.01. (1911) DOI10.1515/crll.1911.140.1
  18. Shapiro, H. S., Shields, A. L., 10.2307/2372892, Amer. J. Math. 83 (1961), 513-532. (1961) Zbl0112.29701MR0133446DOI10.2307/2372892
  19. Shapiro, H. S., Shields, A. L., 10.1007/BF01162379, Math. Zeit. 80 (1962), 217-229. (1962) Zbl0115.06301MR0145082DOI10.1007/BF01162379
  20. Styan, G. P. H., 10.1016/0024-3795(73)90023-2, Linear Algebra 6 (1973), 217-240. (1973) MR0318177DOI10.1016/0024-3795(73)90023-2
  21. Shields, A. L., Wallen, J. L., 10.1512/iumj.1971.20.20062, Indiana Univ. Math. J. 20 (1971), 777-799. (1971) Zbl0207.13801MR0287352DOI10.1512/iumj.1971.20.20062

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