For a collection E of dyadic intervals, a Banach space X, and p ∈ (1, 2] we assume the upper lp estimates

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

We use Tsirelson's Banach space ((2]) to deene an F P-ideal which refutes a conjecture of Mazur and Kechris (see 12, 9, 8]).

Let X be a (real or complex) Banach space, its dual Banach space will be denoted by X *. We use standard notation and terminology of Banach space theory, see J.Lindenstrauss and L.Tzafriri [LT]. By a subspace we mean a linear, but not necessarily closed, subspace. We also assume some knowledge of general topology and ordinal numbers, see P.S.Aleksandrov[A]. Definition 1.1. Let A be a subset of ...

Let G be a locally compact group. We use the canonical operator space structure on the spaces L(G) for p ∈ [1,∞] introduced by G. Pisier to define operator space analoguesOAp(G) of the classical Figà-Talamanca–Herz algebrasAp(G). If p ∈ (1,∞) is arbitrary, then Ap(G) ⊂ OAp(G) such that the inclusion is a contraction; if p = 2, then OA2(G) ∼= A(G) as Banach spaces spaces, but not necessarily as ...

It is shown that a Banach space E has type p if and only for some (all) d ≥ 1 the Besov space B ( 1 p − 1 2 )d p,p (R ;E) embeds into the space γ(L2(Rd), E) of γ-radonifying operators L2(Rd) → E. A similar result characterizing cotype q is obtained. These results may be viewed as E-valued extensions of the classical Sobolev embedding theorems.

We use Tsirelson’s Banach space ([2]) to define an Fσ P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).

Column and row operator spaces — which we denote by COL and ROW, respectively — over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p, p ∈ (1,∞) with 1 p + 1 p = 1, we use the operator space structure on CB(COL(L ′ (G))) to equip the Figà-Talamanca–Herz algebra Ap(G) with ...

Let P be cone Banach space E, A, K are two mappings in P, A accretive, K s k-set contraction, then fixed point index defined for mapping -A+K, some fixed point theorems are also deduced.

We show that the centraliser of the space of n-fold symmetric injective tensors, n ≥ 2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spac...