Cobos, FernandoFernández-Cabrera, Luz M.Martínez, AntónPustylnik, Evgeniy2023-06-202023-06-202002J. Bergh and J. Lofstrom. Interpolation spaces. An introduction (Springer, 1976). Y. Brudnyi and N. Krugljak. Interpolation functors and interpolation spaces, vol. 1 (Amsterdam: North-Holland, 1991). F. Cobos and E. Pustylnik. On strictly singular and strictly co-singular embeddings between Banach lattices of functions. Math. Proc. Camb. Phil. Soc. 133 (2002). (In the press.) F. Cobos, A. Manzano and A. Martínez. Interpolation theory and measures related to operator ideals. Q. J. Math. (2) 50 (1999), 401{416. F. Cobos, A. Manzano, A. Martínez and P. Matos. On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals. Proc. R. Soc. Edinb. A 130 (2000), 971{989. F. Cobos, M. Cwikel and P. Matos. Best possible compactness results of Lions{Peetre type. Proc. Edinb.Math. Soc. 44 (2001), 153{172. A. A. Dmitriev. The interpolation of one-dimensional operators. Vorone·zGos. Univ. Trudy Nau·cn.-Issled. Inst. Mat. VGU Vyp. 11 Sb. Statej Funkcional. Analysis i Prilozen 11 (1973), 31{43. (In Russian.) D. E. Edmunds and H. Triebel.Functionspaces, entropynumbers anddi® erential operators(Cambridge University Press, 1996). S. Goldberg. Unbounded linear operators (McGraw-Hill, 1966). A. Grothendieck. Sur certain sous-espaces vectoriels de Lp . Can. J. Math. 6 (1954), 158{160. S. Heinrich. Closed operator ideals and interpolation. J. Funct. Analysis 35 (1980), 397{411. J. L. Lions and J. Peetre. Sur une classe d’ espaces d’interpolation. Inst. Hautes Etudes Sci. Publ. Math. 19 (1964), 5{68. A. Pelczy¶nski. On strictly singular and strictly co-singular operators. I and II. Bull. Acad. Polon. Sci. S¶er. Sci. Math. Astronom. Phys. 13 (1965), 31{36; 37{41. A. Pietsch. Operator ideals (Amsterdam: North-Holland, 1980). E. Pustylnik. On optimal interpolation and some interpolation properties of Orlicz spaces.Sov.Math. Dokl. 27 (1983), 333{336. E. Pustylnik. Embedding functions and their role in interpolation theory. Abstract Appl. Analysis 1 (1996), 305{325. W. Rudin. Functional analysis (McGraw-Hill, 1973). I. Singer. Bases inBanach spaces, I (Springer, 1970). I. Singer. Bases inBanach spaces, II (Springer, 1981). H. Triebel. Interpolationtheory, functionspaces, di® erential operators (Amsterdam: North-Holland, 1978).0308-210510.1017/S0308210500001645https://hdl.handle.net/20.500.14352/57223We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J -functionals of interpolation theory.engjournal articlehttp://journals.cambridge.org/download.php?file=%2FPRM%2FPRM132_02%2FS0308210500001645a.pdf&code=4cbb92http://www.cambridge.org/restricted access517.98Real InterpolationCompact OperatorsOperator IdealMathematicsAppliedAnálisis funcional y teoría de operadores