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Haar null and non-dominating sets

Sławomir Solecki (2001)

Fundamenta Mathematicae

We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of ω ω . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain...

Hereditarily finitely decomposable Banach spaces

V. Perenczi (1997)

Studia Mathematica

A Banach space is said to be H D n if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of H D n spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex H D n , then dim ( ℒ ( X ) / S ( X ) ) ≤ n 2 , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic division ring....

Hyers-Ulam constants of Hilbert spaces

Taneli Huuskonen, Jussi Väısälä (2002)

Studia Mathematica

The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.

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