A note on lineability
英文摘要:
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
G. Botelho, D. Diniz, D. Pellegrino, E. Teixeira
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
In this note we solve, except for extremely pathological cases, a question posed by Puglisi and Seoane-Sepulveda on the lineability of the set of bounded non-absolutely summing linear operators. We also show how the idea of the proof can be adapted to several related situations.
In this note we prove an abstract version of a result from 2002 due to Delgado and Piñero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear setting. In a final section we investigate the size of the set of non uniformly dominated sets of linear operators under the point of view of lineability.
Pointwise linear separation property and infinite pointwise dense lineability
本文推广了无穷稠密线性概念中的准则,并引入探讨了局部线性概念。
Among other results we investigate $\left( α,β\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.
Let $m,n$ be positive integers. In this short note we prove that the set of all continuous and surjective functions from $\mathbb{R}^{m}$ to $\mathbb{R}^{n}$ contains (excluding the 0 function) a $\mathfrak{c}$-dimensional vector space. This result is optimal in terms of dimension.
A Quest for Convergence: Exploring Series in Non-Linear Environments
本文扩展了2019年提出的[S]-线性概念,在F-空间补集背景下刻画了线性,并在赋范空间和p-Banach空间中给出了否定结果,深化了对拓扑向量空间中奇异线性性质的理解。
On strong algebrability of families of non-measurable functions of two variables
本文在代数性方向上改进了Natkaniec关于两变量不可测函数族的可线性性结果,证明其多数类包含具有$2^{\mathfrak{c}}$个生成元的自由代数。
In this short note we present some new results concerning cotype and absolutely summing multilinear operators.
In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.
In this note we show that the well known coincidence results for scalar-valued homogeneous polynomials can not be generalized in some natural directions.
We show that positive absolutely norm attaining operators can be characterized by a simple property of their spectra. This result clarifies and simplifies a result of Ramesh. As an application we characterize weighted shift operators which are absolutely norm attaining.
In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear.
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 the real numbers $r,s$ with $1\leq s\leq r<\infty$. This improve a result obtained in \cite{DanielT}.
In this note we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators. We connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar results obtained via the complex interpolation method.
This short note has a twofold purpose: (i) to solve the question that motivates a recent paper of D. Popa on multilinear variants of Pietsch's composition theorem for absolutely summing operators. More precisely, we remark that there is a natural perfect extension of Pietsch's composition theorem to the multilinear and polynomial settings. This fact was overlooked in the aforementioned paper; (ii) to investigate extensions of some results of the aforementioned paper for particular situations, mainly by exploring cotype properties of the spaces involved.
Almost sure linear independence of absolutely continuous Hilbert space-valued random vectors with respect to a special class of Hilbert space probability measures
本文研究无限维 Hilbert 空间中随机向量的线性无关性,证明在有限维子空间相对概率测度可忽略时,绝对连续分布可保证无需约束张成空间的随机维数。
In this note we prove that in a metric measure space $(X, d, m)$ verifying the measure contraction property with parameters $K \in \mathbb{R}$ and $1< N< \infty$, any optimal transference plan between two marginal measures is induced by an optimal map, provided the first marginal is absolutely continuous with respect to $m$ and the space itself is essentially non-branching. In particular this shows that there exists a unique transport plan and it is induced by a map.
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