Fréchet frames, general definition and expansions

Details Fréchet frames, general definition and expansions Fréchet frames, general definition and expansions

2012-01-10

arxiv.org/abs/1201.2096v1

Mathematics

Functional Analysis

Scientific paper

We define an $(X_1,\Theta, X_2)$-frame with Banach spaces $X_2\subset X_1$, $\|\cdot\|_1 \leq \|\cdot\|_2$, and a $BK$-space $(\Theta, ||| \cdot |||$. Then by the use of decreasing sequences of Banach spaces $\{X_s\}_{s=0}^\infty$ and $\{\Theta_s\}_{s=0}^\infty$, we define a general Fr\'echet frame on the Fr\'echet space $X_F=\bigcap_{s=0}^\infty X_s$. The main assertion gives expansions of elements of $X_F$ and its dual $X_F^*$, as well of $X_s$ and $X_s^*$.

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