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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the theory of fundamental norming bounded biorthogonal systems in Banach spaces


Author: Paolo Terenzi
Journal: Trans. Amer. Math. Soc. 299 (1987), 497-511
MSC: Primary 46B15
DOI: https://doi.org/10.1090/S0002-9947-1987-0869217-4
MathSciNet review: 869217
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Abstract: Let $ X$ and $ Y$ be quasi complementary subspaces of a separable Banach space $ B$ and let $ ({z_n})$ be a sequence complete in $ X$. Then

(a) there exists a uniformly minimal norming $ M$-basis $ ({x_n})$ of $ X$ with $ {x_m} \in \operatorname{span} {({z_n})_{n \geqslant {q_m}}}$ for every $ m$, $ {q_m} \to \infty $;

(b) if $ ({x_n})$ is a uniformly minimal norming $ M$-basis of $ X$, there exists a uniformly minimal norming $ M$-basis of $ B$ which is an extension of $ ({x_n})$;

(c) there exists a uniformly minimal norming $ M$-basis $ ({x_n}) \cup ({y_n})$ of $ B$ with $ ({x_n}) \subset X$ and $ ({y_n}) \subset Y$.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0869217-4
Article copyright: © Copyright 1987 American Mathematical Society