On an inclusion between operator ideals

Manuel A. Fugarolas

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 209-212
  • ISSN: 0011-4642

Abstract

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Let 1 ≤ q < p < ∞ and 1 / r : = 1 / p max ( q / 2 , 1 ) . We prove that ℒ r , p ( c ) , the ideal of operators of Geľfand type l r , p , is contained in the ideal Π p , q of ( p , q ) -absolutely summing operators. For q > 2 this generalizes a result of G. Bennett given for operators on a Hilbert space.

How to cite

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Fugarolas, Manuel A.. "On an inclusion between operator ideals." Czechoslovak Mathematical Journal 61.1 (2011): 209-212. <http://eudml.org/doc/197217>.

@article{Fugarolas2011,
abstract = {Let $ 1\le q <p < \infty $ and $1/r := 1/p \max (q/2, 1)$. We prove that $\{\mathcal \{L\}\}_\{r,p\}^\{(c)\}$, the ideal of operators of Geľfand type $l_\{r,p\}$, is contained in the ideal $\Pi _\{p,q\}$ of $(p,q)$-absolutely summing operators. For $q>2$ this generalizes a result of G. Bennett given for operators on a Hilbert space.},
author = {Fugarolas, Manuel A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {operator ideals; $s$-numbers; operator ideal; -number},
language = {eng},
number = {1},
pages = {209-212},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On an inclusion between operator ideals},
url = {http://eudml.org/doc/197217},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Fugarolas, Manuel A.
TI - On an inclusion between operator ideals
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 209
EP - 212
AB - Let $ 1\le q <p < \infty $ and $1/r := 1/p \max (q/2, 1)$. We prove that ${\mathcal {L}}_{r,p}^{(c)}$, the ideal of operators of Geľfand type $l_{r,p}$, is contained in the ideal $\Pi _{p,q}$ of $(p,q)$-absolutely summing operators. For $q>2$ this generalizes a result of G. Bennett given for operators on a Hilbert space.
LA - eng
KW - operator ideals; $s$-numbers; operator ideal; -number
UR - http://eudml.org/doc/197217
ER -

References

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  1. Bennett, G., 10.4064/sm-55-1-27-40, Studia Math. 55 (1976), 27-40. (1976) Zbl0338.47013MR0420297DOI10.4064/sm-55-1-27-40
  2. Bennett, G., Goodman, V., Newman, C. M., 10.2140/pjm.1975.59.359, Pacific J. Math. 59 (1975), 359-365. (1975) Zbl0325.47018MR0393085DOI10.2140/pjm.1975.59.359
  3. Bergh, J., Löfström, J., Interpolation Spaces, Springer, Berlin (1976). (1976) 
  4. Carl, B., 10.4064/sm-69-2-143-148, Studia Math. 69 (1980), 143-148. (1980) Zbl0468.47012MR0604346DOI10.4064/sm-69-2-143-148
  5. König, H., 10.1007/BF01351495, Math. Ann. 233 (1978), 35-48. (1978) MR0482266DOI10.1007/BF01351495
  6. König, H., Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel (1986). (1986) MR0889455
  7. Peetre, J., Sparr, G., 10.1007/BF02417949, Ann. Mat. Pura Appl. 92 (1972), 217-262. (1972) Zbl0237.46039MR0322529DOI10.1007/BF02417949
  8. Pietsch, A., 10.1007/BF01364141, Math. Ann. 247 (1980), 149-168. (1980) Zbl0428.47027MR0568205DOI10.1007/BF01364141
  9. Pietsch, A., Operator Ideals, North-Holland, Amsterdam (1980). (1980) Zbl0455.47032MR0582655
  10. Pietsch, A., Eigenvalues and s -numbers, Cambridge Univ. Press (1987). (1987) Zbl0615.47019MR0890520
  11. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam (1978). (1978) Zbl0387.46033MR0503903

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