RT Journal Article
T1 The natural rearrangement invariant structure on tensor products
A1 Fernández González, Carlos
A1 Palazuelos Cabezón, Carlos
A1 Pérez García, David
AB We prove that the only rearrangement invariant (r.i.) spaces for which there exists a crossnorm verifying that the tensor product of these spaces preserves the "natural" r.i. space structure, in the sense that it makes the multiplication operator B a topological isomorphism, are the Lp spaces.
PB Elsevier
SN 0022-247X
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50306
UL https://hdl.handle.net/20.500.14352/50306
LA eng
NO Z. Altshuler, Characterization of co and lp among Banach spaces with symmetric basis, Israel J. Math. 24 (1976) 39–44.T. Andô, On products of Orlicz spaces, Math. Ann. 140 (1960) 174–186.S.V. Astashkin, Tensor product in symmetric function spaces, Collect. Math. 48 (1997) 375–391.S.V. Astashkin, L. Maligranda, E.M. Semenov, Multiplicator space and complemented subspaces of rearrangement invariant space, J. Funct. Anal. 202 (2003) 247–276.A. Defant, K. Floret, Tensor Norms and Operator Ideals, North-Holland, Amsterdam, 1993.A. Defant, D. Pérez-García, A tensor norm preserving unconditionality for Lp-spaces, Trans. Amer. Math. Soc., in press.D.H. Fremlin, Tensor products of Archimedean vector lattices, Amer. J. Math. 94 (1972) 777–798.D.H. Fremlin, Tensor products of Banach lattices, Math. Ann. 211 (1974) 87–106.B.R. Gelbaum, J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961) 1281–1286.F.L. Hernandez, E.M. Semenov, Subspaces generated by translations in rearrangement invariant spaces, J. Funct. Anal. 169 (1999) 52–80.J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I and II, Springer-Verlag, 1996.M. Milman, Some new function spaces and their tensor product, Notas Mat. 20 (1978) 1–128.M. Milman, Tensor products of function spaces, Bull. Amer. Math. Soc. 82 (1976) 626–628.M. Milman, Embeddings of Lorentz–Marcinkiewicz spaces with mixed norms, Anal. Math. 4 (3) (1978) 215–223.M. Milman, Embeddings of L(p, q) spaces and Orlicz spaces with mixed norms, Notas Mat. 13 (1977) 1–7.R. O’Neil, Integral transforms and tensor products on Orlicz spaces and L(p, q) spaces, J. Anal. Math. 21 (1968) 1–276.C.J. Read, When E and E[E] are isomorphic, in: Geometry of Banach Spaces, Strobl, 1989, in: London Math. Soc. Lecture Note Ser., vol. 158, Cambridge Univ. Press, Cambridge, 1990, pp. 245–252.A. Torchinsky, Interpolation of operations and Orlicz classes, Studia Math. 59 (2) (1976/1977) 177–207.
NO MEC FPU Fellowship
NO I+D MCYT
NO Complutense-Santander
NO Comunidad de Madrid
DS Docta Complutense
RD 15 may 2024