## Primariness of some spaces of continuous functions.(English)Zbl 0734.46012

Summary: J. Roberts and the author have recently shown that, under the continuum hypothesis, the Banach space $$\ell_{\infty}/c_ 0$$ is primary. Since this space is isometrically isomorphic to the space $$C(\omega^*)$$ of continuous scalar functions on $$\omega^*=\beta \omega -\omega$$, it is quite natural to consider the question of primariness also for the spaces of continuous vector functions on $$\omega^*$$. The present paper contains some partial results in that direction. In particular, from our results it follows that $$C(\omega^*,C(K))$$ is primary for any infinite metrizable compact space K (without assuming the CH).

### MSC:

 46B25 Classical Banach spaces in the general theory 46B45 Banach sequence spaces 46E40 Spaces of vector- and operator-valued functions 46E15 Banach spaces of continuous, differentiable or analytic functions 03E50 Continuum hypothesis and Martin’s axiom
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