Each operator in L (lp,lr) (1 ≤ r < p < ∞) is compact.
It is known that each bounded operator from lp → lris compact. The purpose of this paper is to present a very simple proof of this useful fact.
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Embedding sums into products of Banach spaces.
Jesús M. Fernández Castillo (1992)
Collectanea Mathematica
Equality of coarse topologies in inverse transformations
M. Burnecki (1996)
Acta Universitatis Carolinae. Mathematica et Physica
Equivalence of multi-norms [Book]
H. G. Dales, M. Daws, H. L. Pham, P. Ramsden (2014)
Equivalences involving (p,q)-multi-norms
Oscar Blasco, H. G. Dales, Hung Le Pham (2014)
Studia Mathematica
We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.
Erratum to the paper: Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces published in Czech. Math. J. vol. 57 (132), No. 2 (2007), 763–776
Erhan Çalışkan (2010)
Czechoslovak Mathematical Journal
Extension and lifting of weakly continuous polynomials
Raffaella Cilia, Joaquín M. Gutiérrez (2005)
Studia Mathematica
We show that a Banach space X is an ℒ₁-space (respectively, an -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an -space.
Extension of bilinear forms from subspaces of -spaces.
Castillo, Jesús M.F., García, Ricardo, Jaramillo, Jesús A. (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
Extension of multilinear operators on Banach spaces.
Félix Cabello Sánchez, R. García, I. Villanueva (2000)
Extracta Mathematicae
These notes deal with the extension of multilinear operators on Banach spaces. The organization of the paper is as follows. In the first section we study the extension of the product on a Banach algebra to the bidual and some related structures including modules and derivations. Tha approach is elementary and uses the classical Arens' technique. Actually most of the results of section 1 can be easily derived from section 2. In section 2 we consider the problem of extending multilinear forms on a...
Extreme points in tensor products and a theorem of de Leeuw
J. Johnson (1971)
Studia Mathematica
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