Representations of the spaces C ( N ) H k , p ( N )

A. Albanese; V. Moscatelli

Studia Mathematica (2000)

  • Volume: 142, Issue: 2, page 135-148
  • ISSN: 0039-3223

Abstract

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We give a representation of the spaces C ( N ) H k , p ( N ) as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that C ( N ) H k , 2 ( N ) is isomorphic to the sequence space s l 2 ( l 2 ) , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

How to cite

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Albanese, A., and Moscatelli, V.. "Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$." Studia Mathematica 142.2 (2000): 135-148. <http://eudml.org/doc/216793>.

@article{Albanese2000,
abstract = {We give a representation of the spaces $C^∞(ℝ^N) ∩ H^\{k,p\}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^\{k,2\}(ℝ^N)$ is isomorphic to the sequence space $s^\{ℕ\} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.},
author = {Albanese, A., Moscatelli, V.},
journal = {Studia Mathematica},
keywords = {Fréchet structure; isomorphism; isomorphy class; Fréchet space; Montel subspaces},
language = {eng},
number = {2},
pages = {135-148},
title = {Representations of the spaces $C^∞(ℝ^N) ∩ H^\{k,p\}(ℝ^N)$},
url = {http://eudml.org/doc/216793},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Albanese, A.
AU - Moscatelli, V.
TI - Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 2
SP - 135
EP - 148
AB - We give a representation of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^{k,2}(ℝ^N)$ is isomorphic to the sequence space $s^{ℕ} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.
LA - eng
KW - Fréchet structure; isomorphism; isomorphy class; Fréchet space; Montel subspaces
UR - http://eudml.org/doc/216793
ER -

References

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  1. [A] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975. 
  2. [AA] A. A. Albanese, Montel subspaces of Fréchet spaces of Moscatelli type, Glasgow Math. J. 39 (1997), 345-350. Zbl0923.46011
  3. [AMM1] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces C m ( Ω ) H k , p ( Ω ) , Math. Proc. Cambridge Philos. Soc. 120 (1996), 489-498. 
  4. [AMM2] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces C m ( N ) H k , p N , in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 11-20. 
  5. [AMM3] A. A. Albanese, G. Metafune and V. B. Moscatelli, On the spaces C k ( ) L p ( ) , Arch. Math. (Basel) 68 (1997), 228-232. Zbl0876.46022
  6. [AM] A. A. Albanese and V. B. Moscatelli, A method of construction of Fréchet spaces, in: Functional Analysis, P. K. Jain (ed.), Narosa Publishing House, New Delhi, 1998, 1-8. Zbl0949.46002
  7. [BB] K. D. Bierstedt and J. Bonet, Stefan Heinrich's density condition for Fréchet spaces and the characterization of distinguished Köthe echelon spaces, Math. Nachr. 135 (1988), 149-180. Zbl0688.46001
  8. [B] J. Bonet, Intersections of Fréchet Schwartz spaces and their duals, Arch. Math. (Basel) 68 (1997), 320-325. Zbl0916.46001
  9. [BD] J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (suppl.) (1989), 77-92. Zbl0757.46001
  10. [BT] J. Bonet and J. Taskinen, Non-distinguished Fréchet function spaces, Bull. Soc. Roy. Sci. Liège 58 (1989), 483-490. Zbl0711.46001
  11. [DK] S. Dierolf and Khin Aye Aye, On projective limits of Moscatelli type, in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 105-118. Zbl0902.46001
  12. [MT] P. Mattila and J. Taskinen, Remarks on bases in a Fréchet function space, Rev. Mat. Univ. Complut. Madrid 6 (1993), 93-99. Zbl0814.46005
  13. [M] V. B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66. Zbl0407.46002
  14. [S] R. T. Seeley, Extension of C functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626. Zbl0127.28403
  15. [T1] J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev. Mat. Univ. Complut. Madrid 6 (1993), 101-120. Zbl0804.46027
  16. [T2] J. Taskinen, Examples of non-distinguished Fréchet spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 75-88. Zbl0632.46002
  17. [V1] M. Valdivia, Topics in Locally Convex Spaces, North-Holland Math. Stud. 67, 1982. 
  18. [V2] M. Valdivia, A characterization of totally reflexive Fréchet spaces, Math. Z. 200 (1989), 327-346. Zbl0683.46008

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