Bicomplex Riesz-Fischer Theorem

Details Bicomplex Riesz-Fischer Theorem Bicomplex Riesz-Fischer Theorem

2011-09-15

arxiv.org/abs/1109.3429v2

Mathematics

Functional Analysis

arXiv admin note: text overlap with arXiv:1006.5017

Scientific paper

This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in previous articles on the topic. Besides obtaining a Best Approximation Theorem, the main purpose of this paper is to obtain a bicomplex analogue of the Riesz-Fischer Theorem. There are many statements of the Riesz-Fischer (R-F) Theorem in the literature, some are equivalent, some are consequences of the original versions. The one referred to in this paper is the R-F Theorem which establishes that the spaces $l^2$ and $L^2[a,b]$ are isomorphic and isometric.

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