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On the serial completion of deleted Schauder bases by domain adjustment

Author: Ben-Ami Braun
Journal: Proc. Amer. Math. Soc. 44 (1974), 427-431
MSC: Primary 46E30
MathSciNet review: 0355565
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Abstract: Given a Schauder basis in a Banach function space of a specified type, one can delete any finite number of elements of the basis and still preserve serial totality by making an arbitrarily small adjustment of the domain.

References [Enhancements On Off] (What's this?)

  • [1] Ben-Ami Braun, An extension of a result by Talalyan on the representation of measurable functions by Schauder bases, Proc. Amer. Math. Soc. 34 (1972), 440-446. MR 45 #4138. MR 0295070 (45:4138)
  • [2] A. A. Talaljan, On the convergence almost everywhere of subsequences of partial sums of general orthogonal series, Izv. Akad. Nauk Armyan SSR Fiz.-Mat. Nauk 10 (1957), no. 3, 17-34. (Russian) MR 19, 742. MR 0089940 (19:742b)
  • [3] -, The representations of measurable functions by series, Uspehi Mat. Nauk 15 (1960), no. 5 (95), 77-141 = Russian Math. Surveys 15 (1960), no. 5, 75-136. MR 23 #A2704. MR 0125401 (23:A2704)

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Keywords: Schauder basis, completion, series representation
Article copyright: © Copyright 1974 American Mathematical Society

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