Geodesic
Inclusion Indices of Quasi-Banach Spaces
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 99-117.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
Vengono studiati gli indici di inclusione per spazi quasi-Banach. Prima si considera il caso di spazi di funzioni su $[0, 1]$, poi il caso degli spazi di successioni e, infine, si sviluppa un approccio astratto, usando indici definiti dalla scala degli spazi di interpolazione reale generata da una coppia quasi-Banach. 
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Cobos, Fernando; Fernández-Cabrera, Luz M.; Manzano, Antonio; Martínez, Antón. Inclusion Indices of Quasi-Banach Spaces. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 99-117. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a6/

[1] J. Bastero - H. Hudzik - A.M. Steinberg, On smallest and largest spaces among rearrangement-invariant p-Banach function spaces ($0 < p < 1$). Indag. Mathem., N.S. 2 (1991), 283-288. | DOI | MR | Zbl

[2] C. Bennett - R. Sharpley, Interpolation of Operators (Academic Press, 1988). | MR | Zbl

[3] J. Bergh - J. Löfström, Interpolation Spaces. An introduction (Springer, 1976). | MR

[4] F. Cobos - M. Cwikel - P. Matos, Best possible compactness results of Lions-Peetre type. Proc. Edinburgh Math. Soc., 44 (2001), 153-172. | DOI | MR | Zbl

[5] F. Cobos - A. Manzano - A. Martínez, Interpolation theory and measures related to operator ideals. Quart. J. Math. Oxford, 50 (1999), 401-416. | DOI | MR

[6] F. Cobos - A. Manzano - A. Martínez - P. Matos, On interpolation of strictly singular operators, strictly cosingular operators and related operator ideals. Proc. Royal Soc. Edinburgh, 130A (2000), 971-989. | DOI | MR | Zbl

[7] F. Cobos - E. Pustylnik, On strictly singular and strictly cosingular embeddings between Banach lattices of functions. Math. Proc. Camb. Phil. Soc., 133 (2002), 183-190. | DOI | MR | Zbl

[8] A. A. Dmitriev, 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). | MR

[9] L.M. Fernández-Cabrera, Inclusion indices of function spaces and applications. Math. Proc. Camb. Phil. Soc. 137 (2004), 665-674. | DOI | MR

[10] L.M. Fernández-Cabrera, On inclusion indices of function spaces. In: Proc. Inter. Symposium on Banach and Function Spaces, p. 185-203, (Yokohama Publishers, 2004). | MR

[11] L.M. Fernández-Cabrera, F. Cobos, F.L. Hernández, V.M. Sánchez, Indices defined by interpolation scales and applications. Proc. Royal Soc. Edinburgh, 134A (2004), 695-717. | DOI | MR

[12] A. García Del Amo - F.L. Hernández - C. Ruiz, Disjointly strictly singular operators and interpolation. Proc. Royal Soc. Edinburgh, 126A (1996), 1011-1026. | DOI | MR | Zbl

[13] A. García Del Amo - F.L. Hernández - V.M. Sánchez - E. M. Semenov, Disjointly strictly-singular inclusions between rearrangement invariant spaces. J. London Math. Soc., 62 (2000), 239-252. | DOI | MR

[14] S. Goldberg, Unbounded Linear Operators (McGraw-Hill, 1966). | MR | Zbl

[15] N.J. Kalton, Orlicz sequence spaces without local convexity. Math. Proc. Camb. Phil. Soc., 81 (1977), 253-277. | DOI | MR | Zbl

[16] S.G. Kreiïn - Ju.I. Petunin - E.M. Semenov, (Amer. Math. Soc., Providence, R.I., 1982). | MR

[17] J. Lindenstrauss - L. Tzafriri, `Classical Banach Spaces', Vol. II, `Function Spaces' ( Springer, 1979). | MR | Zbl

[18] L. Maligranda, Indices and interpolation. Dissertationes Math., 234 (1985), 1-54. | MR | Zbl

[19] L. Maligranda - M. Mastylo, Notes on non-interpolation spaces. J. Approx. Theory, 56 (1989), 333-347. | DOI | MR | Zbl

[20] A. Pietsch, Operator Ideals (North-Holland, 1980). | MR

[21] E. Pustylnik, Interpolation theorems in massives of Banach spaces. Soviet Math. Dokl., 16 (1975), 1359-1363. | Zbl

[22] E. Pustylnik, Embedding functions and their role in interpolation theory. Abstract Appl. Analysis, 1 (1996), 305-325. | fulltext EuDML | DOI | MR | Zbl

[23] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978. | MR | Zbl