J ul 2 00 4 Incomparable , non isomorphic and minimal Banach spaces
نویسنده
چکیده
A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E0 does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes and has an isomorphically homogeneous subsequence.
منابع مشابه
m at h . FA ] 1 5 M ay 2 00 0 BANACH EMBEDDING PROPERTIES OF NON - COMMUTATIVE L p - SPACES
Let N and M be von Neumann algebras. It is proved that L p (N) does not Banach embed in L p (M) for N infinite, M finite, 1 ≤ p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class Cp embeds in L p (N) for N infinite). Theorem. Let 1 ≤ p < 2 and let X be a Banach space with a spanning set (x ij) so that for some C ≥ 1, (i) any row or column...
متن کاملJ an 2 00 2 On the number of non - isomorphic subspaces of a Banach space . Valentin Ferenczi and Christian Rosendal December 2001
We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following: let X be a Banach space with an unconditional basis {ei}i∈N; then either there exists a perfect set P of infinite subsets of N such that for any two distinct A,B ∈ P, [ei]i∈A ≇ [ei]i∈B , or for a residual set of infinite subsets A of N, [ei]i∈A is isomorphic to X, and in that case, X is is...
متن کاملOn Hereditariness for Real and Complex Interpolation
Every isometric property of Banach spaces preserved by real or complex interpolation is subspace-hereditary, and every isomorphic property of separable Banach spaces so preserved is quotient-hereditary. Introduction Many properties of Banach spaces are known to pass to interpolation spaces obtained from the real k-method of interpolation or from the complex method, completeness itself being the...
متن کامل2 4 A pr 1 99 2 A note on unconditional structures in weak
We prove that if a non-atomic separable Banach lattice in a weak Hilbert space, then it is lattice isomorphic to L2(0, 1). Introduction This note is to be considered as an addendum to [3], where an extensive study of Banach lattices, which are weak Hilbert spaces, was made. We prove that if a non-atomic separable Banach lattice is a weak Hilbert space then it is lattice isomorphic to L2(0, 1). ...
متن کامل