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On the algebraic properties of the H n 2 , 1 2 spaces

Sergiu Klainerman, Matei Machedon (1997/1998)

Séminaire Équations aux dérivées partielles

We investigate the multiplicative properties of the spaces H n 2 , 1 2 As in the case of the classical Sobolev spaces H n 2 this space does not form an algebra. We investigate instead the space H n 2 L , more precisely a subspace of it formed by products of solutions of the homogeneous wave equation with data in H n 2 .

On the Banach-Mazur distance between continuous function spaces with scattered boundaries

Jakub Rondoš (2023)

Czechoslovak Mathematical Journal

We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant 2 appearing in the Amir-Cambern theorem may be replaced by 3 for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the...

On the Banach-Stone problem

Jyh-Shyang Jeang, Ngai-Ching Wong (2003)

Studia Mathematica

Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of then T can be written as a weighted composition...

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