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Some reiteration results for interpolation methods defined by means of polygons


Cobos, Fernando and Fernandez-Cabrera, Luz M. and Martin, Joaquim (2008) Some reiteration results for interpolation methods defined by means of polygons. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 138 . pp. 1179-1195. ISSN 0308-2105

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We continue the research on reiteration results between interpolation methods associated to polygons and the. real method. Applications are given to N-tuples of function spaces, or spaces or hounded linear operators and Banach algebras.

Item Type:Article
Uncontrolled Keywords:Compact-Operators; Spaces; Duality; Mathematics, Applied; Mathematics
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:14960

1 C. Bennett and R. Sharpley. Interpolation of operators(Boston, MA: Academic, 1988).

2 J. Bergh and J. L¨ofstr¨om. Interpolation spaces: an introduction (Springer, 1976).

3 E. A. Bishop. Holomorphic completion, analytic continuation, and the interpolation of seminorms. Annals Math. 78 (1963), 468–500.

4 Y. Brudnyˇı and N. Krugljak. Interpolation functors and interpolation spaces, vol. 1 (Amsterdam: North-Holland, 1991).

5 F. Cobos and L. M. Fern´andez-Cabrera. Factoring weakly compact homomorphisms, interpolation of Banach algebras and multilinear interpolation. Banach Center Publ. 79 (2008), 57–69.

6 F. Cobos and P. Fern´andez-Mart´ınez. A duality theorem for interpolation methods associated to polygons. Proc. Am. Math. Soc. 121 (1994), 1093–1101.

7 F. Cobos, P. Fern´andez-Mart´ınez and A. Mart´ınez. On reiteration and the behaviour of weak compactness under certain interpolation methods. Collectanea Math. 50 (1999), 53–72.

8 F. Cobos, P. Fern´andez-Mart´ınez, A. Mart´ınez and Y. Raynaud. On duality between Kand J-spaces. Proc. Edinb. Math. Soc. 42 (1999), 43–63.

9 F. Cobos, P. Fern´andez-Mart´ınez and T. Schonbek. Norm estimates for interpolation methods defined by means of polygons. J. Approx. Theory 80 (1995), 321–351.

10 F. Cobos, T. K¨uhn and T. Schonbek. One-sided compactness results for Aronszajn–Gagliardo functors. J. Funct. Analysis 106 (1992), 274–313.

11 F. Cobos and J. Mart´ın. On interpolation of function spaces by methods defined by means of polygons. J. Approx. Theory 132 (2005), 182–203.

12 F. Cobos and M. Milman. On a limit class of approximation spaces. Numer. Func. Analysis Optim. 11 (1990), 11–31.

13 F. Cobos and J. Peetre. Interpolation of compact operators: the multidimensional case. Proc. Lond. Math. Soc. 63 (1991), 371–400.

14 F. Cobos and I. Resina. Representation theorems for some operator ideals. J. Lond. Math. Soc. 39 (1989), 324–334.

15 S. Ericsson. Certain reiteration and equivalence results for the Cobos–Peetre polygon interpolation method. Math. Scand. 85 (1999), 301–319.

16 D. L. Fernandez. Interpolation of 2n Banach spaces. Studia Math. 45 (1979), 175–201.

17 D. L. Fernandez. Interpolation of 2d Banach spaces and the Calder´on space X(E). Proc. Lond. Math. Soc. 56 (1988), 143–162.

18 L. M. Fern´andez-Cabrera and A. Mart´ınez. Interpolation methods defined by means of polygons and compact operators. Proc. Edinb. Math. Soc. 50 (2007), 653–671.

19 I. C. Gohberg and M. G. Krein. Introduction to the theory of linear nonselfadjoint operators(Providence, RI: American Mathematical Society, 1969).

20 M. E. Gomez and M. Milman. Extrapolation spaces and almost-everywhere convergence of singular integrals. J. Lond. Math. Soc. 34 (1986), 305–316. Polygon interpolation methods 1195

21 S. Kaijser. Interpolation of Banach algebras and open sets. Integ. Eqns Operat. Theory 41 (2001), 189–222.

22 V. I. Macaev. A class of completely continuous operators. Sov. Math. Dokl. 2 (1961), 972–975.

23 M. Milman. Extrapolation and optimal decompositions, Lecture Notes in Mathematics, vol. 1580 (Springer, 1994).

24 V. I. Ovchinnikov. Interpolation in symmetrically normed ideals of operators that act in different spaces. Funkt. Analiz Prilozhen. 28 (1994), 80–82. (In Russian.)

25 V. I. Ovchinnikov. Lions–Peetre construction for couples of operator spaces. Russ. J. Math. Phys. 3 (1995), 407–410.

26 G. Sparr. Interpolation of several Banach spaces. Annali Mat. Pura Appl. 99 (1974), 247–316.

27 H. Triebel. Theory of function spaces (Basel: Birkh¨auser, 1983).

28 H. Triebel. Theory of function spaces. II (Basel: Birkh¨auser, 1992).

29 H. Triebel. Interpolation theory, function spaces, differential operators, 2nd edn (Leipzig: Barth, 1995). (See also 1st edn (Amsterdam: North-Holland, 1978).)

30 H. Triebel. Theory of function spaces. III (Basel: Birkh¨auser, 2006).

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