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The general form of local bilinear functions

Milan Práger (1993)

Applications of Mathematics

The scalar product of the FEM basis functions with non-intersecting supports vanishes. This property is generalized and the concept of local bilinear functional in a Hilbert space is introduced. The general form of such functionals in the spaces L 2 ( a , b ) and H 1 ( a , b ) is given.

The inclusion theorem for multiple summing operators

David Pérez-García (2004)

Studia Mathematica

We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

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