It is proved that the Disc Algebra does not contain a complemented subspace isomorphic to the space C(k)(Td) of k times continuously differentiable functions on the d-dimensional torus ( k = 1, 2, ... ; d = 2, 3, ... ). Introduction. Recall two interesting problems concerning the space q 1)(T2 ) of continuously differentiable functions on the 2-dimensional torus T2 . (I) Is C(1)(T2 ) isomorphic...

Following results of Bourgain and Gorelik we show that the spaces lp, 1 < p < ∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0, then it is isomorphic to c0. We show also that there are B...

For any positive integer r, denote by Pr the set of all integers γ ∈ Z having at most r prime divisors. We show CPr (T), the space of all continuous functions on the circle T whose Fourier spectrum lies in Pr, contains a complemented copy of `1. In particular, CPr (T) is not isomorphic to C(T), nor to the disc algebra A(D). A similar result holds in the L1 setting. For any set of “frequencies” ...

New concepts related to approximating a Lipschitz function between Banach spaces by a ne functions are introduced Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X Y for which any Lipschitz function from X to Y can be so approx imated is obtained This is applied to the study of Lipschitz and uniform quotient mapp...

We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1 ≤ p <∞) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae allows us to prove some James-type results for atomic decompositions: an uncon...

We introduce the theory IHR of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IHR are derived using Lack’s approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IHR is isomorphic to the PROP of linear relations (i.e. subspac...

In this talk we discuss a new connection between convex geometry and the theory of Lp-spaces. It appears that intersection bodies, one the main objects of convex geometry, are directly related to the concept of embedding of normed spaces in Lp with p < 0. This allows to get new geometric results by extending different facts about Lp-spaces to negative values of p. We present several application...

In this paper we prove that if a Grassmann space Δ = GrA(m,h,K) of the h–subspaces of an affine space A = AG(m,K) has an embedding e into a projective space PG(n,K′) over a skew–field K′, and e satisfies two suitable conditions (α) and (β), then K and K′ are isomorphic fields and Δ is, up to projections, an affine Grassmannian. Mathematics Subject Classification (2000). 51A45; 51M35.

A joint order detection and blind estimation algorithm for single input multiple output channels is proposed. By exploiting the isomorphic relation between the channel input and output subspaces, it is shown that the channel order and channel impulse response are uniquely determined by finite least squares smoothing error sequence in the absence of noise. The proposed subspace algorithm is show...

We characterize positive topological entropy for quasi-state space homeomorphisms induced from C∗-algebra automorphisms in terms of dynamically generated subspaces isomorphic to l1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as ...