Coincidences for multiple summing mappings

On scalar-valued nonlinear absolutely summing mappings

In this note we show that the well known coincidence results for scalar-valued homogeneous polynomials can not be generalized in some natural directions.

On the Maurey--Pisier and Dvoretzky--Rogers theorems

A famous theorem due to Maurey and Pisier asserts that for an infinite dimensional Banach space $E$, the infumum of the $q$ such that the identity map $id_{E}$ is absolutely $\left( q,1\right) $-summing is precisely $\cot E$. In the same direction, the Dvoretzky--Rogers Theorem asserts $id_{E}$ fails to be absolutely $\left( p,p\right) $-summing, for all $p\geq1$. In this note, among other results, we unify both theorems by charactering the parameters $q$ and $p$ for which the identity map is absolutely $\left( q,p\right)$-summing. We also provide a result that we call \textit{strings of coinc…

Almost summing mappings

We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing multilinear mappings coincides with the whole space of continuous multilinear mappings.

An integral formula for multiple summing norms of operators

We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show inclusion and coincidence results for multiple summing mappings. We also present some contraction properties and compute or estimate the limit orders of this class of operators.

Cotype and nonlinear absolutely summing mappings

In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every $n$% -linear mapping from $\mathcal{L}_{\infty}$-spaces into $\mathbb{K}$ is $% (2;2,...,2,\infty)$-summing and also shown that every $n$-linear mapping from $\mathcal{L}_{\infty}$-spaces into $F$ is $(q;2,...,2)$-summing whenever $F$ has cotype $q.$ We also give new examples of analytic summing mappings and polynomial and multilinear versions of a linear Extrapolation Theorem.

Cohen strongly p-summing holomorphic mappings on Banach spaces

Let $E$ and $F$ be complex Banach spaces, $U$ be an open subset of $E$ and $1\leq p\leq\infty$. We introduce and study the notion of a Cohen strongly $p$-summing holomorphic mapping from $U$ to $F$, a holomorphic version of a strongly $p$-summing linear operator. For such mappings, we establish both Pietsch domination/factorization theorems and analyse their linearizations from $\mathcal{G}^\infty(U)$ (the canonical predual of $\mathcal{H}^\infty(U)$) and their transpositions on $\mathcal{H}^\infty(U)$. Concerning the space $\mathcal{D}_p^{\mathcal{H}^\infty}(U,F)$ formed by such mappings and …

格序列空间与求和映射

Lattice sequence spaces and summing mappings

本研究推进了正求和算子理论，通过结合正强p-可和、正无条件p-可和及正弱p-可和序列空间，刻画了正强(p; q)-求和、正(p; q)-求和与正Cohen (p; q)-核算子类，并利用张量算子的连续性进行描述。

Coincidence points of Mappings in Banach Spaces

In this article we prove an existence theorem for coincidence points of mappings in Banach spaces. This theorem generalizes the Kantorovich fixed point theorem.

On the composition ideals of Lipschitz mappings

We study in this paper some property of Lipschitz mappings which admit factorization through an operator ideal. We try to construct Lipschitz cross-norms from known tensor norms in order to represent certain classes of Lipschitz mappings. Inspired by the definition of p-summing linear operators we introduce a new concpet in the the category of Lipschitz mappings that is called strictly Lipschitz p-summing.

Multiple summing mpas : coordinatewise summability, inclusion theorems and p-Sidon sets

We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of $p$-Sidon sets.

Summability of multilinear mappings: Littlewood, Orlicz and beyond

In this paper we prove a plenty of new results concerning summabililty properties of multilinear mappings between Banach spaces, such as an extension of Littlewood's 4/3 Theorem. Among other features, it is shown that every continuous n-linear form on the disc algebra or the Hardy space is (1;2,...,2)-summing, the role of the Littlewood-Orlicz property in the theory is established and the interplay with almost summing multilinear mappings is explored.

When is the Haar measure a Pietsch measure for nonlinear mappings?

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.

Absolutely summing linear operators into spaces with no finite cotype

Given an infinite-dimensional Banach space $X$ and a Banach space $Y$ with no finite cotype, we determine whether or not every continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing for almost all choices of $p$ and $q$, including the case $p=q$. If $X$ assumes its cotype, the problem is solved for all choices of $p$ and $q$. Applications to the theory of dominated multilinear mappings are also provided.

复单位圆盘上的 p-求和 Bloch 映射

p-Summing Bloch mappings on the complex unit disc

本文定义复单位圆盘到 Banach 空间的 $p$-求和 Bloch 映射，证明其 Möbius 不变性与零保持子空间的内射理想性质，并建立 Bloch 型 Pietsch、Maurey 定理及分子空间对偶刻画。

Coincidence and Common Fixed Point Results for Generalized $α$-$ψ$ Contractive Type Mappings with Applications

A new, simple and unified approach in the theory of contractive mappings was recently given by Samet \emph{et al.} (Nonlinear Anal. 75, 2012, 2154-2165) by using the concepts of $α$-$ψ$-contractive type mappings and $α$-admissible mappings in metric spaces. The purpose of this paper is to present a new class of contractive pair of mappings called generalized $α$-$ψ$ contractive pair of mappings and study various fixed point theorems for such mappings in complete metric spaces. For this, we introduce a new notion of $α$-admissible w.r.t $g$ mapping which in turn generalizes the concept of $g$-m…

A new approach to coincidence and common fixed points under a homotopy of families of mappings in $b$-metric spaces

In this paper we derive coincidence and common fixed point results under order homotopies of families of mappings in preordered $b$-metric spaces.

On the existence of coincidence and common fixed point of two rational type contractions and an application in dynamical programming

In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous existing theorems in the literature besides furnishing some illustrative examples for our results. Finally, our results applies, in particular, to the study of solvability of functional equations arising in dynamic programming.

Common fixed points for three or four mappings via common fixed point for two mappings

In this paper, we shall show that some coincidence point and common fixed point results for three or four mappings could easily be obtained from the corresponding fixed point results for two mappings.

Existence and uniqueness to several kinds of differential equations using the Coincidence Theory

The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of results will be applied to obtain the existence of solutions for some classes of ordinary differential equations.

Common fixed point theorems in $C^*$-algebra-valued metric spaces

In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are given.