Some inequalities involving upper bounds for some matrix operators. I

R. Lashkaripour; D. Foroutannia

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 553-572
  • ISSN: 0011-4642

Abstract

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In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces l p ( w ) and Lorentz sequence spaces d ( w , p ) , which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on l p spaces, see [1] and [2].

How to cite

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Lashkaripour, R., and Foroutannia, D.. "Some inequalities involving upper bounds for some matrix operators. I." Czechoslovak Mathematical Journal 57.2 (2007): 553-572. <http://eudml.org/doc/31146>.

@article{Lashkaripour2007,
abstract = {In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces $l_p(w)$ and Lorentz sequence spaces $d(w,p)$, which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on $l_p$ spaces, see [1] and [2].},
author = {Lashkaripour, R., Foroutannia, D.},
journal = {Czechoslovak Mathematical Journal},
keywords = {inequality; norm; summability matrix; Hausdorff matrix; Nörlund matrix; weighted mean matrix; weighted sequence space and Lorentz sequence space; summability matrix; Hausdorff matrix; Nörlund matrix; weighted mean matrix; upper bounds; matrix operators; sequence spaces; Lorentz sequence spaces},
language = {eng},
number = {2},
pages = {553-572},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some inequalities involving upper bounds for some matrix operators. I},
url = {http://eudml.org/doc/31146},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Lashkaripour, R.
AU - Foroutannia, D.
TI - Some inequalities involving upper bounds for some matrix operators. I
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 553
EP - 572
AB - In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces $l_p(w)$ and Lorentz sequence spaces $d(w,p)$, which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on $l_p$ spaces, see [1] and [2].
LA - eng
KW - inequality; norm; summability matrix; Hausdorff matrix; Nörlund matrix; weighted mean matrix; weighted sequence space and Lorentz sequence space; summability matrix; Hausdorff matrix; Nörlund matrix; weighted mean matrix; upper bounds; matrix operators; sequence spaces; Lorentz sequence spaces
UR - http://eudml.org/doc/31146
ER -

References

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  9. 10.1017/S0017089500020061, Glasgow Math. J. 42 (2000), 211–223. (2000) MR1763740DOI10.1017/S0017089500020061
  10. Norms of certain operators on weighted l p spaces and Lorentz sequence spaces, J. Inequalities in Pure and Applied Mathematics, 3, Issue 1, Article 6 (2002). (2002) MR1888921
  11. Lower bounds and norms of operators on Lorentz sequence spaces, Doctoral dissertation (Lancaster, 1997). 
  12. Transpose of the Weighted Mean operators on Weighted Sequence Spaces, WSEAS Transaction on Mathematics, Issue 4, 4 (2005), 380–385. (2005) MR2119309
  13. Lower Bounds for Matrices on Weighted Sequence Spaces, Journal of Sciences Islamic Republic of IRAN, 18 (2007), 49–56. (2007) MR2499829
  14. On bounds for weighted norms for matrices and integral operators, Linear Algebra and Appl. 326 (2001), 121–135. (2001) MR1815954

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