Inclusion Indices of Quasi-Banach Spaces

Fernando Cobos; Luz M. Fernández-Cabrera; Antonio Manzano; Antón Martínez

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 1, page 99-117
  • ISSN: 0392-4041

Abstract

top
We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on [ 0 , 1 ] , then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.

How to cite

top

Cobos, Fernando, et al. "Inclusion Indices of Quasi-Banach Spaces." Bollettino dell'Unione Matematica Italiana 10-B.1 (2007): 99-117. <http://eudml.org/doc/290371>.

@article{Cobos2007,
abstract = {We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on $[0, 1]$, then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.},
author = {Cobos, Fernando, Fernández-Cabrera, Luz M., Manzano, Antonio, Martínez, Antón},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {99-117},
publisher = {Unione Matematica Italiana},
title = {Inclusion Indices of Quasi-Banach Spaces},
url = {http://eudml.org/doc/290371},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Cobos, Fernando
AU - Fernández-Cabrera, Luz M.
AU - Manzano, Antonio
AU - Martínez, Antón
TI - Inclusion Indices of Quasi-Banach Spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/2//
PB - Unione Matematica Italiana
VL - 10-B
IS - 1
SP - 99
EP - 117
AB - We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on $[0, 1]$, then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.
LA - eng
UR - http://eudml.org/doc/290371
ER -

References

top
  1. BASTERO, J. - HUDZIK, H. - STEINBERG, A.M., On smallest and largest spaces among rearrangement-invariant p-Banach function spaces ( 0 < p < 1 ). Indag. Mathem., N.S. 2 (1991), 283-288. Zbl0754.46021MR1149681DOI10.1016/0019-3577(91)90016-Z
  2. BENNETT, C. - SHARPLEY, R., Interpolation of Operators (Academic Press, 1988). Zbl0647.46057MR928802
  3. BERGH, J. - LÖFSTRÖM, J., Interpolation Spaces. An introduction (Springer, 1976). MR482275
  4. COBOS, F. - CWIKEL, M. - MATOS, P., Best possible compactness results of Lions-Peetre type. Proc. Edinburgh Math. Soc., 44 (2001), 153-172. Zbl1004.46019MR1879216DOI10.1017/S0013091598001163
  5. COBOS, F. - MANZANO, A. - MARTÍNEZ, A., Interpolation theory and measures related to operator ideals. Quart. J. Math. Oxford, 50 (1999), 401-416. MR1726783DOI10.1093/qjmath/50.200.401
  6. COBOS, F. - MANZANO, A. - MARTÍNEZ, A. - MATOS, P., On interpolation of strictly singular operators, strictly cosingular operators and related operator ideals. Proc. Royal Soc. Edinburgh, 130A (2000), 971-989. Zbl1007.46060MR1800087DOI10.1017/S0308210500000524
  7. COBOS, F. - PUSTYLNIK, E., On strictly singular and strictly cosingular embeddings between Banach lattices of functions. Math. Proc. Camb. Phil. Soc., 133 (2002), 183-190. Zbl1011.47014MR1900261DOI10.1017/S0305004102005881
  8. DMITRIEV, A. A., The interpolation of one-dimensional operators. Voronež Gos. Univ. Trudy Naučn.-Issled. Inst. Mat. VGU Vyp. 11Sb. Statej Funkcional. Anal. i Prilozen, 11 (1973), 31-43 (Russian). MR477805
  9. FERNÁNDEZ-CABRERA, L.M., Inclusion indices of function spaces and applications. Math. Proc. Camb. Phil. Soc.137 (2004), 665-674. MR2055054DOI10.1017/S0305004103007503
  10. FERNÁNDEZ-CABRERA, L.M., On inclusion indices of function spaces. In: Proc. Inter. Symposium on Banach and Function Spaces, p. 185-203, (Yokohama Publishers, 2004). MR2147606
  11. FERNÁNDEZ-CABRERA, L.M., COBOS, F., HERNÁNDEZ, F.L., SÁNCHEZ, V.M., Indices defined by interpolation scales and applications. Proc. Royal Soc. Edinburgh, 134A (2004), 695-717. MR2079801DOI10.1017/S0308210500003437
  12. GARCÍA DEL AMO, A. - HERNÁNDEZ, F.L. - RUIZ, C., Disjointly strictly singular operators and interpolation. Proc. Royal Soc. Edinburgh, 126A (1996), 1011-1026. Zbl0860.47024MR1415819DOI10.1017/S0308210500023222
  13. GARCÍA DEL AMO, A. - HERNÁNDEZ, F.L. - SÁNCHEZ, V.M. - SEMENOV, E. M., Disjointly strictly-singular inclusions between rearrangement invariant spaces. J. London Math. Soc., 62 (2000), 239-252. MR1772184DOI10.1112/S0024610700001150
  14. GOLDBERG, S., Unbounded Linear Operators (McGraw-Hill, 1966). Zbl0148.12501MR200692
  15. KALTON, N.J., Orlicz sequence spaces without local convexity. Math. Proc. Camb. Phil. Soc., 81 (1977), 253-277. Zbl0345.46013MR433194DOI10.1017/S0305004100053342
  16. KREIÏN, S.G. - PETUNIN, JU.I. - SEMENOV, E.M., (Amer. Math. Soc., Providence, R.I., 1982). MR649411
  17. LINDENSTRAUSS, J. - TZAFRIRI, L., `Classical Banach Spaces', Vol. II, `Function Spaces' ( Springer, 1979). Zbl0403.46022MR540367
  18. MALIGRANDA, L., Indices and interpolation. Dissertationes Math., 234 (1985), 1-54. Zbl0566.46038MR820076
  19. MALIGRANDA, L. - MASTYLO, M., Notes on non-interpolation spaces. J. Approx. Theory, 56 (1989), 333-347. Zbl0668.46039MR990348DOI10.1016/0021-9045(89)90123-8
  20. PIETSCH, A., Operator Ideals (North-Holland, 1980). MR582655
  21. PUSTYLNIK, E., Interpolation theorems in massives of Banach spaces. Soviet Math. Dokl., 16 (1975), 1359-1363. Zbl0339.46026
  22. PUSTYLNIK, E., Embedding functions and their role in interpolation theory. Abstract Appl. Analysis, 1 (1996), 305-325. Zbl0943.46009MR1485579DOI10.1155/S1085337596000164
  23. TRIEBEL, H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978. Zbl0387.46033MR503903

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.