Abstract
A basis\(\left\{ {x_n } \right\}_{n = 1}^\infty \) is constructed inc 0 such that there exists no bounded linear projection ofc 0 onto the subspace spanned by a certain subsequence\(\left\{ {x_{n_k } } \right\}_{k = 1}^\infty \) of\(\left\{ {x_n } \right\}_{n = 1}^\infty \).
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References
B. Grünbaum,Projection constants, Trans. Amer. Math. Soc.95 (1960), 441.
J. Lindenstrauss,Extension of compact operators, Mem. Amer. Math. Soc.48 (1964).
A. Pełczyński,Some open questions in functional analysis, a lecture given to Louisiana State University (dittoed notes).
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This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice.
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Zippin, M. On a certain basis inc 0 . Israel J. Math. 4, 199–204 (1966). https://doi.org/10.1007/BF02760078
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DOI: https://doi.org/10.1007/BF02760078