Ascoli Theorems and the Exponential Map

Invariant Subspaces and the Exponential Map

Bounded operators with no non-trivial closed invariant subspace have been constructed by P. Enflo [6]. In fact, there exist bounded operators on the space 1 with no non-trivial closed invariant subset [12]. It is still unknown, however, if such operators exist on reflexive Banach spaces, or on the separable Hilbert space. The main result of this note (Theorem 1) asserts that the existence of an...

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

An Operator Arzelà-ascoli Theorem

We generalize the Arzelà-Ascoli theorem to the setting of matrix order unit spaces, extending the work of Antonescu-Christensen on unital C∗algebras. This gives an affirmative answer to a question of Antonescu and Christensen.

An Asymmetric Arzelà-Ascoli Theorem

An Arzelà-Ascoli theorem for asymmetric metric spaces (sometimes called quasi-metric spaces) is proved. One genuinely asymmetric condition is introduced, and it is shown that several classic statements fail in the asymmetric context if this assumption is dropped.

Conformality, the Exponential Function, and World Map Projections

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