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

A. Albanese; V. Moscatelli

Studia Mathematica (2000)

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

Abstract

top
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.

How to cite

top

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

top
  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 ( ℝ N ) ∩ H k , p ℝ 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 ( ℝ ) ∩ L p ( ℝ ) , 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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.