Interpolating subspaces in l1-spaces

l1-SPREADING MODELS IN SUBSPACES OF MIXED TSIRELSON SPACES

We investigate the existence of higher order l-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space X = T [(θn,Sn) ∞ n=1]: (1) Every block subspace of X contains an l-Sω-spreading model, (2) The Bourgain l-index Ib(Y ) = I(Y ) > ω ω for any block subspace Y of X, (3) limm lim supn θm+n/θn > 0 an...

Optimal Interpolating Spaces

In this paper we study the existence and characterization of spaces which are images of minimal-norm projections that are required to interpolate at given functionals and satisfy additional shape-preserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This investigation leads to concrete solutions in classical settings and, as examples, n will be determi...

ε-weakly Chebyshev subspaces and quotient spaces

Interpolating Hereditarily Indecomposable Banach Spaces

A Banach space X is said to be Hereditarily Indecomposable (H.I.) if for any pair of closed subspaces Y , Z of X with Y ∩ Z = {0}, Y + Z is not a closed subspace. (Throughout this section by the term “subspace” we mean a closed infinite-dimensional subspace of X .) The H.I. spaces form a new and, as we believe, fundamental class of Banach spaces. The celebrated example of a Banach space with no...

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...