Spaceability of the set of bounded linear non-absolutely summing\n operators in Quasi-Banach sequence spaces

2019/02/25 by Daniel Tomaz, Tomaz, Daniel
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1902.09668

Abstract

In the short note we prove that for every 0<p<1, there exists an infinite\ndimensional closed linear subspace of \L\(\n\ℓ_p;\ℓ_p\) every nonzero element of which is non\n(r,s)-absolutely summing operator for the real numbers r,s with 1\≤\ns\≤ r<\∞. This improve a result obtained in citeDanielT.\n

Related

• Lineability of the set of bounded linear non-absolutely summing operators
• Spaceability of sets of non-injective maps
• Some properties of almost summing operators
• On the size of the set of unbounded multilinear operators between Banach spaces
• Absolutely summing multilinear operators on ℓ_p spaces