Spaceability in Banach and quasi-Banach sequence spaces

Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-\bigcup _{q\in\Gamma}\ell_{q}(X)$, where $\Gamma$ is any subset of $(0,\infty]$, and $E-c_{0}(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.Comment: 9 page

Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials

[EN] We draw a fundamental compendium of the most valuable results of the theory of summing linear operators and detail those that are not shared by known multilinear and polynomial extensions of absolutely summing linear operators. The lack of such results in the theory of non-linear summing operators justifies the introduction of a class of polynomials and multilinear operators that satisfies at once all related non-linear results. Surprisingly enough, this class, defined by means of a summing inequality, happens to be the well known ideal of composition with a summing operator.D. Pellegrino acknowledges with thanks the support of CNPq Grant 401735/2013-3-PVE (Linha 2)-Brazil. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2012-36740-C02-02.Pellegrino, D.; Rueda, P.; Sánchez Pérez, EA. (2016). 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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

Lineability of the set of bounded linear non-absolutely summing operators

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.Comment: 7 page

Avaliação da resistência à ferrugem em progênies de cafeeiro F4 obtidas por cruzamentos de 'icatu' com catimor.

Com o objetivo de selecionar progênies de cafeeiro resistentes à ferrugem foram instalados e conduzidos experimentos em Três Pontas, São Sebastião do Paraíso e Machado. Foram avaliadas 17 progênies desenvolvidas pelo programa de Melhoramento Genético do Cafeeiro em Minas Gerais, coordenado pela EPAMIG e obtidas pelo cruzamento ?Icatu? x Catimor, e a cultivar Rubi MG 1192 utilizada como testemunha. O delineamento foi o de blocos casualizados com três repetições. Foram analisadas as características incidência da ferrugem no primeiro semestre de 2006.Os resultados obtidos permitem verificar que as progênies avaliadas apresentam variabilidade para a resistência a ferrugem, isso é confirmado pelas estimativas da herdabilidade que foram de boa magnitude, chegando até o valor de 92,8%. Essa condição aliada à baixa incidência da doença apresentada por algumas progênies, demonstrou que é possível selecionar progênies superiores em relação à resistência a ferrugem na população estudada