Acknowledgment of priority to the paper "On self-conjugate Banach spaces''
R. Sztencel, P. Zaremba (1988)
Colloquium Mathematicae
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Displaying similar documents to “On self-conjugate Banach spaces”
Acknowledgment of priority to the paper "On self-conjugate Banach spaces''
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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.
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Non-normal elements in Banach *-algebras
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Let A be a Banach *-algebra with an identity, continuous involution, center Z and set of self-adjoint elements Σ. Let h ∈ Σ. The set of v ∈ Σ such that (h + iv)ⁿ is normal for no positive integer n is dense in Σ if and only if h ∉ Z. The case where A has no identity is also treated.