相关论文: Numerical index of absolute sums of Banach spaces

We improve upon on a limit theorem for numerical index for large classes of Banach spaces including vector valued $\ell_p$-spaces and $\ell_p$-sums of Banach spaces where $1\leq p \leq \infty$. We first prove $ n_1(X) = \displaystyle \lim_m…

We present an example of a Banach space whose numerical index is strictly greater than the numerical index of its dual, giving a negative answer to a question which has been latent since the beginning of the seventies. We also show a…

We show that for real Banach spaces that are either separable or dual spaces, the Lipschitz numerical index coincides with the classical (linear) numerical index. This result provides partial evidence toward the question posed by Wang,…

We introduce the notion of index of summability for pairs of Banach spaces; for Banach spaces E; F, this index plays the role of a kind of measure of how the m-homogeneous polynomials from E to F are far from being absolutely summing. In…

It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k \subset E$ one has \[ \summ_k \noo x_k \rrm \kl c_E \pl \sup_{\eps_k \pm 1} \noo \summ_k…

The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any…

We introduce a second numerical index for real Banach spaces with non-trivial Lie algebra, as the best constant of equivalence between the numerical radius and the quotient of the operator norm modulo the Lie algebra. We present a number of…

We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real $L_p$-space for $3/2\leq p\leq 3$.

We provide some new consequences on the Lipschitz numerical radius and index which were introduced recently. More precisely, we give some renorming results on the Lipschitz numerical index, introduce a concept of Lipschitz numerical radius…

The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming $\ell_p$-sums of Banach spaces, and obtain…

The numerical index of a Banach space is a geometric constant relating the numerical radius of bounded linear operators to their standard operator norm. In this paper, we study the continuity of the numerical index under two distinct…

In this paper we survey some recent results concerning the numerical index $n(\cdot)$ for large classes of Banach spaces, including vector valued $\ell_p$-spaces and $\ell_p$-sums of Banach spaces where $1\leq p < \infty$. In particular by…

In the short note we prove that for every $0<p<1$, there exists an infinite dimensional closed linear subspace of $\mathcal{L}\left( \ell_{p};\ell_{p}\right) $ every nonzero element of which is non $(r,s)$-absolutely summing operator for…

Let $E_{1},...,E_{m},F$ be Banach spaces. The index of summability of $\left(E_{1}\times\cdots\times E_{m},F\right) $ is a kind of measure of how far the $m$-linear operators $T:E_{1}\times\cdots\times E_{m}\rightarrow F$ are from being…

We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp…

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 $E_0$ does not reduce to…

We show that a Banach space with numerical index one cannot enjoy good convexity or smoothness properties unless it is one-dimensional. For instance, it has no WLUR points in its unit ball, its norm is not Frechet smooth and its dual norm…

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We study the convexity of…