Revistes Catalanes amb Accés Obert (RACO)

Espacios de Fréchet de generación débilmente compacta

Manuel Valdivia


Let $E$ be a Fréchet space whose topology is defined by a fundamental system of seminorms: $$\parallel \cdot\parallel_1 \leq\parallel\cdot \parallel_2\leq\cdots\leq\parallel\cdot\parallel_n\leq\cdots$$ Let $\mu$ be the first ordinal number whose cardinal number coincides with the density character or $E$. Then, if $E$ is generated by an absolutely convex weakly compact subset $W$, there exists a resolution of the identity in $E$ $$\{P_\alpha:\omega\leq\alpha\leq\mu\}$$ such that $$\parallel P_\alpha\parallel_m=1,\quad P_\alpha(W)\subset W,\quad \omega\leq\alpha\leq\mu,\quad m=1,2,\cdots$$

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