RT Journal Article T1 Weakly compact bilinear operators among real interpolation spaces A1 Cobos, Fernando A1 Fernández Cabrera, Luz M. AB We show a necessary and sufficient condition for weak compactness of bilinear operators interpolated by the real method. This characterization does not hold for interpolated operators by the complex method. PB Elsevier SN 0022-247X YR 2022 FD 2022-11-08 LK https://hdl.handle.net/20.500.14352/72630 UL https://hdl.handle.net/20.500.14352/72630 LA eng NO [1] B. Beauzamy, Espaces d'Interpolation Réels: Topologie et Géométrie, Springer, Lecture Notes in Math. 666, Berlin, 1978.[2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.[3] Y. Brudny and N. Krugljak, Interpolation Functors and Interpolation Spaces, Vol. 1, North-Holland, Amsterdam, 1991.[4] A.P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964) 113-190.[5] F. Cobos, L.M. Fernández-Cabrera A. Manzano and A. Martínez, Real interpolation and closed operator ideals, J. Math. Pures el Appl. 83 (2004) 417-432.[6] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, Interpolation of compact bilinear operators among quasi-Banach spaces and applications, Math. Nachr. 291 (2018) 2168-2187.[7] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, On compactness results of Lions-Peetre type for bilinear operators, Nonlinear Anal. 199 (2020) 111951.[8] F. Cobos, L.M. Fernández-Cabrera and A. Martínez, On interpolation of weakly compact bilinear operators, Math. Nachr. 295 (2022) 1279-1291.[9] F. Cobos, T. Kühn and T. Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Anal. 106 (1992) 274-313.[10] F. Cobos and A. Martínez, Remarks on interpolation properties of the measure of weak non-compactness and ideal variations, Math. Nachr. 208 (1999) 93-100.[11] F. Cobos and A. Martínez, Extreme estimates for interpolated operators by the real method, J. London Math. Soc. 60 (1999) 860-870.[12] M. Cwikel, Real and complex interpolation and extrapolation of compact operators, Duke Math. J. 65 (1992) 333-343.[13] A. Defand and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies 176, Amsterdam, 1993.[14] J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge Univ. Press, Cambridge, 1995.[15] J. Diestel and J. J. Ulh Jr., Vector Measures, Amer. Math. Soc. Surveys No. 15, Providence, Rhode Island, 1977.[16] D.L. Fernandez and E.B. da Silva, Interpolation of bilinear operators and compactness, Nonlinear Anal. 73 (2010) 526-537.[17] L.M. Fernández-Cabrera and A. Martínez, On interpolation properties of compact bilinear operators, Math. Nachr. 290 (2017) 1663-1677.[18] L.M. Fernández-Cabrera and A. Martínez, Real interpolation of compact bilinear operators, J. Fourier Anal. Appl. 24 (2018) 1181-1203.[19] S. Heinrich, Closed operator ideals and interpolation, J. Funct. Anal. 35 (1980) 397-411.[20] J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964) 5-68.[21] L. Maligranda and A. Quevedo, Interpolation of weakly compact operators, Arch. Math. 55 (1990) 280-284.[22] A. Manzano, P. Rueda and E. A. Sánchez-Pérez, Closed injective ideals of multilinear operators, related measures and interpolation, Math. Nachr. 293 (2020) 510-532.[23] A. Manzano, P. Rueda and E. A. Sánchez-Pérez, Closed surjective ideals of multilinear operators and interpolation, Banach J. Math. Anal. 15:27 (2021).[24] M. Mastylo, Interpolation spaces not containing l1, J. Math. Pures et Appl. 68 (1989) 153-162.[25] M. Mastylo, On interpolation of weakly compact operators, Hokkaido Math. J. 22 (1993) 105-114.[26] M. Mastylo and E.B. Silva, Interpolation of compact bilinear operators, Bull. Math. Sci. 10 (2020) 2050002.[27] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.[28] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. NO CRUE-CSIC (Acuerdos Transformativos 2022) DS Docta Complutense RD 29 abr 2024