# On the representation of uncountable symmetric basic sets and its applications

Francisco Hernandez; Stanimir Troyanski

Studia Mathematica (1993)

- Volume: 107, Issue: 3, page 287-304
- ISSN: 0039-3223

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topHernandez, Francisco, and Troyanski, Stanimir. "On the representation of uncountable symmetric basic sets and its applications." Studia Mathematica 107.3 (1993): 287-304. <http://eudml.org/doc/216034>.

@article{Hernandez1993,

abstract = {It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.},

author = {Hernandez, Francisco, Troyanski, Stanimir},

journal = {Studia Mathematica},

keywords = {symmetric basis; Orlicz sequence spaces; Lorentz sequence spaces; uncountable symmetric basic set in an -space with a symmetric basis},

language = {eng},

number = {3},

pages = {287-304},

title = {On the representation of uncountable symmetric basic sets and its applications},

url = {http://eudml.org/doc/216034},

volume = {107},

year = {1993},

}

TY - JOUR

AU - Hernandez, Francisco

AU - Troyanski, Stanimir

TI - On the representation of uncountable symmetric basic sets and its applications

JO - Studia Mathematica

PY - 1993

VL - 107

IS - 3

SP - 287

EP - 304

AB - It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.

LA - eng

KW - symmetric basis; Orlicz sequence spaces; Lorentz sequence spaces; uncountable symmetric basic set in an -space with a symmetric basis

UR - http://eudml.org/doc/216034

ER -

## References

top- [ACL] Z. Altshuler, P. G. Casazza and B. L. Lin, On symmetric basic sequences in Lorentz sequence spaces, Israel J. Math. 15 (1973), 140-155. Zbl0264.46011
- [D₁] L. Drewnowski, On symmetric bases in nonseparable Banach spaces, Studia Math. 85 (1987), 157-161. Zbl0625.46019
- [D_2] L. Drewnowski, On uncountable unconditional bases in Banach spaces, ibid. 90 (1988), 191-196. Zbl0669.46006
- [K] N. Kalton, Orlicz sequence spaces without local convexity, Math. Proc. Cambridge Philos. Soc. 81 (1977), 253-277. Zbl0345.46013
- [KPR] N. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge University Press, 1984.
- [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, 1977. Zbl0362.46013
- [M] V. D. Milman, Geometric theory of Banach spaces I. The theory of bases and minimal systems, Russian Math. Surveys 25 (1970), 111-170.
- [P] N. Popa, Basic sequences and subspaces in Lorentz sequence spaces without local convexity, Trans. Amer. Math. Soc. 263 (1981), 431-456. Zbl0461.46006
- [R] B. Rodriguez-Salinas, Subspaces with symmetric basis in the Orlicz space ${\ell}^{F}\left(I\right)$, preprint.
- [Ro] S. Rolewicz, Metric Linear Spaces, 2nd ed., PWN-Reidel, Warszawa, 1984.
- [T₁] S. Troyanski, On non-separable Banach spaces with a symmetric basis, Studia Math. 53 (1975), 253-263. Zbl0322.46017
- [T_2] S. Troyanski, On representation of uncountable symmetric basic sets, in: Proc. 5th Spring Conference of Math. and Math. Education (Gabrovo 1976), Sofia, 1990, 169-173 (in Russian).

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