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Special symmetries of Banach spaces isomorphic to Hilbert spaces

Jarno Talponen (2010)

Studia Mathematica

We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.

Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure

Ryszard A. Komorowski, Nicole Tomczak-Jaegermann (2002)

Studia Mathematica

It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.

The n -dual space of the space of p -summable sequences

Yosafat E. P. Pangalela, Hendra Gunawan (2013)

Mathematica Bohemica

In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an n -normed space, we are interested in bounded multilinear n -functionals and n -dual spaces. The concept of bounded multilinear n -functionals on an n -normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear n -functionals, introduce the concept of n -dual spaces, and...

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