U-ideals of factorable operators

Kamil John

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 3, page 607-616
  • ISSN: 0011-4642

Abstract

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We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are u -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.

How to cite

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John, Kamil. "U-ideals of factorable operators." Czechoslovak Mathematical Journal 49.3 (1999): 607-616. <http://eudml.org/doc/30509>.

@article{John1999,
abstract = {We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are $u$-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.},
author = {John, Kamil},
journal = {Czechoslovak Mathematical Journal},
keywords = {factorization of linear operators; u-ideal; approximation properties; unconditional basis; factorization of linear operators; -ideal; approximation properties; unconditional basis},
language = {eng},
number = {3},
pages = {607-616},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {U-ideals of factorable operators},
url = {http://eudml.org/doc/30509},
volume = {49},
year = {1999},
}

TY - JOUR
AU - John, Kamil
TI - U-ideals of factorable operators
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 3
SP - 607
EP - 616
AB - We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are $u$-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
LA - eng
KW - factorization of linear operators; u-ideal; approximation properties; unconditional basis; factorization of linear operators; -ideal; approximation properties; unconditional basis
UR - http://eudml.org/doc/30509
ER -

References

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  10. Classical Banach Spaces, Sequence Spaces, EMG 92 Springer Verlag (1977). (1977) MR0500056
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  12. Operator ideals, Berlin, Deutscher Verlag der Wissenschaften, 1978. (1978) Zbl0405.47027MR0519680
  13. Counterexamples to a conjecture of Grothendieck, Acta Mat. 151 (1983), 180–208. (1983) Zbl0542.46038MR0723009
  14. Duality and Geometry of spaces of compact operators, Functional Analysis: Surveys and Recent Results III, Math. Studies 90, North Holland, 1984, pp. 59–78. (1984) Zbl0573.46007MR0761373

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