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ISSN 1088-6826(e) ISSN 0002-9939(p)

Subspaces of with more than one complex structure

Author(s): Razvan Anisca
Journal: Proc. Amer. Math. Soc. 131 (2003), 2819-2829.
MSC (2000): Primary 46B20
Posted: January 28, 2003
MathSciNet review: 1974339
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Abstract: We propose a method of constructing explicit Banach spaces not isomorphic to their complex conjugates as subspaces of a natural class of Banach spaces. In particular, it is shown that , for $1\leq p<2$ , contains real subspaces with at least two non-isomorphic complex structures.

References:

1.: J. Bourgain, Real isomorphic complex Banach spaces need not be complex isomorphic, Proc. Amer. Math. Soc. 96(1986), 221-226. MR 87b:46012
2.: W. B. Johnson, J. Lindenstrauss and G. Schechtman, On the relation between several notions of unconditional structure, Israel J. Math. 37(1980), 120-129. MR 83f:46015
3.: N. J. Kalton and N. T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255(1979), 1-30. MR 82g:46021
4.: N. J. Kalton, An elementary example of a Banach space not isomorphic to its complex conjugate, Canad. Math. Bull. 38(1995), 218-222. MR 96e:46018
5.: R. Komorowski and N. Tomczak-Jaegermann, Banach spaces without local unconditional structure, Israel J. Math. 89(1995), 205-226. MR 96g:46007
6.: R. Komorowski and N. Tomczak-Jaegermann, Eratum to: Banach spaces without local unconditional structure, Israel J. Math. 105(1998), 85-92. MR 99g:46008
7.: R. Komorowski and N. Tomczak-Jaegermann, Subspaces of and without unconditional structure, Studia Math. 149 (2002), 1-21.
8.: T. Ketonen, On unconditionality in spaces, Annales Academiae Sciendemiae Scientiarum Scientiarum Fennicae, Series A I, Mathematica Dissertationes 35(1981). MR 82h:46020
9.: D. R. Lewis, Finite dimensional subspaces of , Studia Math. 63(1978), 207-212.
10.: J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Sequence spaces, Springer-Verlag, Berlin, 1977. MR 58:17766
11.: J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Function spaces, Springer-Verlag, Berlin, 1979. MR 81c:46001
12.: S. Szarek, A superreflexive Banach space which does not admit complex structure, Proc. Amer. Math. Soc. 97(1986), 437-444. MR 87f:46026
13.: S. Szarek, On the existence and uniqueness of complex structure and spaces with ``few" operators, Trans. Amer. Math. Soc. 293(1986), 339-353. MR 87e:46029
14.: N. Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs 38, Longman Scientific Technical, Harlow, 1989. MR 90k:46039

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Additional Information:

Razvan Anisca
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: anisca@math.ualberta.ca

DOI: 10.1090/S0002-9939-03-06858-8
PII: S 0002-9939(03)06858-8
Received by editor(s): July 17, 2001
Received by editor(s) in revised form: April 3, 2002
Posted: January 28, 2003
Additional Notes: This work was supported by an Izaak Walton Killam Memorial Scholarship at the University of Alberta
Communicated by: David R. Larson
Copyright of article: Copyright 2003, American Mathematical Society

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